aleqsandre xaraziSvilis monacemebi misi SromiTi da samecniero ...

aleqsandre xaraziSvilis monacemebi misi SromiTi da
samecniero saqmianobis Sesaxeb (CV)
aleqsandre beJanis Ze xaraziSvilma 1972 wels warCinebiT daamTavra
iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universitetis
meqanika-maTematikis fakulteti (specialobiT: maTematika).
1972 wlis dekembridan 2006 wlamde igi muSaobda Tsu-s i.vekuas
saxelobis gamoyenebiTi maTematikis institutSi.
1973 wlidan 1976 wlamde igi muSaobda aRniSnuli institutis
umcros mecnier-TanamSromlad.
1974 wels Tsu-s samecniero sabWos sxdomaze man daicva sakandidato
disertacia specialobiT: geometria-topologia (01.01.04).
1976 wlidan 1983 wlamde igi muSaobda Tsu-s i.vekuas saxelobis
gamoyenebiTi maTematikis institutis ufros-mecnier TanamSromlad.
1982 wels man daicva disertacia fizika-maTematikis mecnierebaTa
doqtoris xarisxis mosapoveblad (q.kievSi, ukrainis mecnierebaTa
akademiis maTematikis institutis samecniero sabWos sxdomaze),
specialobiT: maTematikuri analizi (01.01.01).
1983 wlidan 2006 wlamde igi muSaobda Tsu-s i.vekuas saxelobis
gamoyenebiTi maTematikis institutis diskretuli maTematikis
ganyofilebis gamgis Tanamdebobaze.
2005 wlis dekembridan a.xaraziSvili muSaobs saqarTvelos
mecnierebaTa akademiis a.razmaZis maTematikis institutSi, maTematikuri
analizis ganyofilebis mTavari mecnier-TanamSromlis Tanamdebobaze.
2006-2011 wlebSi igi muSaobda i.WavWavaZis saxelmwifo
universitetis fizika-maTematikis fakultetis sruli profesoris
Tanamdebobaze.
a.xaraziSvils gamoqveynebuli aqvs 250-ze meti samecniero Sroma
maTematikaSi (publikaciebis sruli sia CV-is Tan erTvis), maT Soris
ramdenime monografia. es Sromebi exeba Tanamedrove maTematikis
sxvadasxva dargs: simravleTa Teoriasa da usasrulo kombinatorikas,
namdvili cvladis funqciaTa Teorias, zomis Teoriasa da funqcionalur
analizs, amozneqil geometrias. a.xaraziSvilis mier miRebuli
maTematikuri Sedegebi mravaljer iyo citirebuli Sesabamisi dargebis
specialistebis mier (citirebis nusxa CV-is Tan erTvis). misi mTavari
Sromebia: A
1

(1) A.B. Kharazishvili, Applications of Point Set Theory in Real Analysis,
Kluwer Academic Publishers, Dordrecht, 1998;
(2) A.B. Kharazishvili, Transformation Groups and Invariant Measures, World
Scientific Publ. Co., London-Singapore, 1998;
(3) A.B. Kharazishvili, Geometric Aspects of Probability Theory and
Mathematical Statistics, Kluwer Academic Publishers, Dordrecht, 2000 (co-author:
V.V. Buldygin);
(4) A.B. Kharazishvili, Strange Functions in Real Analysis; Marcel Dekker,
Inc., New York-Basel, 2000;
(5) A.B. Kharazishvili, Nonmeasurable Sets and Functions, North-Holland
Mathematics Studies, Elsevier, 2004;
(6) A.B. Kharazishvili, Strange Functions in Real Analysis (second edition,
revised and expanded), Chapman and Hall/CRC, New York, 2006;
(7) A.B. Kharazishvili, Topics in Measure Theory and Real Analysis, Atlantis
Press & World Scientific Publ. Co., London-Singapore, 2009.
(8) A.B. Kharazishvili, Certain types of invariant measures, DAN SSSR, v. 222,
n. 3, 1975, pp. 538-540 (in Russian).
(9) A.B. Kharazishvili, On a nonseparable extension of the Lebesgue measure,
DAN SSSR, v. 226, n. 1, 1976 (in Russian).
(10) A.B. Kharazishvili, To the Sierpinski problem on proper extensions of
invariant measures, DAN SSSR, v. 232, n. 2, 1977 (in Russian).
(11) A.B. Kharazishvili, On nonmeasurable sets, DAN SSSR, v. 232, n. 5,
1977(in Russian).
(12) A.B. Kharazishvili, Equidecomposability of polyhedra with respect to the
group of homotheties and translations, DAN SSSR, v. 236, n. 3, 1977 (in Russian).
(13) A.B. Kharazishvili, On some sigma-algebras, Ukrain. Mathem. Journ., v.
37, n. 2, 1985 (in Russian).
(14) A.B. Kharazishvili, On sets of Vitali's type, Proc. Amer. Math. Soc., v.
118, n. 4, 1993, pp. 1221-1228 (co-authors: J. Cichon, B. Weglorz).
(15) A.B. Kharazishvili, Extending quasi-invariant measures by using subgroups
of a given group, Georgian Mathematical Journal, v. 10, n. 2, 2003, pp. 247 - 255.
(16) A.B. Kharazishvili, On extensions of partial functions, Expositiones
Mathematicae, v. 25, issue 4, 2007, pp. 345-353 (co-author: A. Kirtadze).
(17) A.B. Kharazishvili, Metrical transitivity and nonseparable extensions of
invariant measures, Taiwanese Journal of Mathematics, v. 13, n. 3, 2009.
(18) A.B. Kharazishvili, On sums of real-valued functions with extremely thick
graphs, Expositiones Mathematicae, v. 27, n. 2, 2009, pp. 161-169.
(19) A.B. Kharazishvili, On almost measurable real-valued functions, Studia
Scientiarum Mathematicarum Hungarica, v. 47, n. 2, 2010, pp. 257-266.
(20) A.B. Kharazishvili, A combinatorial problem on translation-invariant
extensions of the Lebesgue measure, Expositiones Mathematicae, v. 29, n. 1, 2011,
pp. 150-158.
2

(21) A.B. Kharazishvili, Measurability properties of Vitali sets, Amer. Math.
Monthly, v. 118, n. 10, 2011, pp. 693-703.
a.xaraziSvili mravaljer iyo miwveuli sazRvargareT, sxvadasxva
saerTaSoriso maTematikur forumSi monawileobis misaRebad (ruseTSi,
ukrainaSi, poloneTSi, CexeTSi, ungreTSi, bulgareTSi, aSS-Si,
safrangeTSi, germaniaSi, meqsikaSi da sxv.). 1994-1998 wlebSi igi
muSaobda loZis universitetSi miwveuli profesoris statusiT.
a.xaraziSvili aris saqarTvelos maTematikosTa kavSiris wevri,
saqarTvelos sabunebismetyvelo mecnierebaTa akademiis wevri da
saqarTvelos mecnierebaTa erovnuli akademiis wevr-korespondenti.
a.xaraziSvili aris ori avtoritetuli saerTaSoriso maTematikuri
Jurnalis redkolegiis wevri: Georgian Mathematical Journal, Journal of
Applied Analysis.
1996 wels a. xaraziSvils mieniWa loZis universitetis (poloneTi)
premia mis mier Sesrulebul naSromTa ciklisaTvis.
2006 wels mas mieniWa mecnierebis istoriis saqarTvelos
sazogadoebis premia.
2008 wels mas mieniWa saqarTvelos mecnierebaTa erovnuli akademiis
akademikos n. musxeliSvilis saxelobis premia.
a. xaraziSvilis xelmZRvanelobiT daculi iqna 7 sakandidato
disertacia da 1 disertacia doqtoris akademiuri xarisxis
mosapoveblad.
3

The Publications of A.B. Kharazishvili
The symbol (*) marks monographs, surveys, theses, or text-
Remark.
books.
1972
[1]. Dispositions on a straight line, on a plane and in a space, Metsniereba
da Tekhnika, n. 3, 1972 (in Georgian).
1973
[2]. On a property of convex hulls, Bull. Acad. Sci. GSSR, v. 71, n. 1, 1973
(in Russian).
[3]. To the problem of illumination, Bull. Acad. Sci. GSSR, v. 71, n. 2,
1973 (in Russian).
[4]. Characteristic properties of parallelepipeds, Bull. Acad. Sci. GSSR, v.
72, n. 1, 1973 (in Russian).
1974
[5]. Some combinatorial properties of subsets of the Euclidean spaces, Thesis,
Izd. Tbil. Gos. Univ., Tbilisi, 1974.
[6]. Absolutely measure zero sets nonmeasurable in the Lebesgue sense, Bull.
Acad. Sci. GSSR, v. 75, n. 2, 1974 (in Russian).
[7]. On extensions of the Lebesgue measure, Bull. Acad. Sci. GSSR, v. 75,
n. 3, 1974 (in Russian).
[8]. Realization of the coloured graphs in Hilbert spaces, Bull. Acad. Sci.
GSSR, v. 76, n. 1, 1974 (in Russian).
1975
[9]. On decompositions of polytopes, Bull. Acad. Sci. GSSR, v. 77, n. 1,
1975 (in Russian).
[10]. On strongly transitive transformation groups, Bull. Acad. Sci. GSSR,
v. 79, n. 1, 1975 (in Russian).
[11]. On sets with the uniqueness property with respect to classes of invariant
measures, Bull. Acad. Sci. GSSR, v. 79, n. 3, 1975 (in Russian).
[12]. On locally conical sets, Bull. Acad. Sci. GSSR, v. 80, n. 1, 1975 (in
Russian).
1

[13]. One example of an invariant measure, DAN SSSR, v. 220, n. 1, 1975
(in Russian).
[14]. On nonelementary measures, DAN SSSR, v. 220, n. 2, 1975 (in
Russian).
[15]. Certain types of invariant measures, DAN SSSR, v. 222, n. 3, 1975,
538-540 (in Russian).
1976
[16]. On a nonseparable extension of the Lebesgue measure, DAN SSSR, v.
226, n. 1, 1976 (in Russian).
[17]. On absolutely nonmeasurable and absolutely negligible sets with respect
to the classes of invariant measures, DAN SSSR, v. 226, n. 2, 1976 (in Russian).
[18]. On intransitivity classes of motion groups of the Euclidean spaces, DAN
SSSR, v. 226, n. 3, 1976 (in Russian).
[19]. On Vitali systems, Bull. Acad. Sci. GSSR, v. 81, n. 2, 1976 (in
Russian).
[20]. On differentiation by Vitali systems, Bull. Acad. Sci. GSSR, v. 82, n.
2, 1976 (in Russian).
[21]. On metrically transitive measures, Bull. Acad. Sci. GSSR, v. 82, n.
3, 1976 (in Russian).
[22]. On extensions of invariant measures, Bull. Acad. Sci. GSSR, v. 83,
n. 3, 1976 (in Russian).
[23]. Transfinite sequences of mappings of infinite sets, Bull. Acad. Sci.
GSSR, v. 84, n. 3, 1976 (in Russian).
1977
[24]. Some applications of Hamel bases, Bull. Acad. Sci. GSSR, v. 85, n.
1, 1977, 17-20 (in Russian).
[25]. Fully symmetric configurations, Bull. Acad. Sci. GSSR, v. 85, n. 2,
1977 (in Russian).
[26]. On mappings of infinite sets, Bull. Acad. Sci. GSSR, v. 86, n. 2, 1977
(in Russian).
[27]. Characterization of rt-sets in Euclidean spaces, Bull. Acad. Sci. GSSR,
v. 86, n. 3, 1977 (in Russian).
[28]. On Π-isomorphisms of binary relations, Bull. Acad. Sci. GSSR, v. 87,
n. 3, 1977, (in Russian).
[29]. Orthogonal simplexes in the four-dimensional space, Bull. Acad. Sci.
GSSR, v. 88, n. 1, 1977 (in Russian).
[30]. On the existence of Borel Π-isomorphisms, Bull. Acad. Sci GSSR, v.
88, n. 3, 1977 (in Russian).
[31]. To the Sierpinski problem on proper extensions of invariant measures,
DAN SSSR, v. 232, n. 2, 1977 (in Russian).
[32]. On nonmeasurable sets, DAN SSSR, v. 232, n. 5, 1977 (in Russian).
2

[33]. Some properties of uniform subsets of the Euclidean plane, DAN SSSR,
v. 235, n. 4, 1977 (in Russian).
[34]. Equidecomposability of polyhedra with respect to the group of homotheties
and translations, DAN SSSR, v. 236, n. 3, 1977 (in Russian).
1978
[35]. Some properties of the centre of symmetry, Bull. Acad. Sci. GSSR, v.
89, n. 1, 1978 (in Russian).
[36]. On the Vitali theorem about nonmeasurable sets, Bull. Acad. Sci.
GSSR, v. 90, n. 1, 1978 (in Russian).
[37]. On relative density points, Bull. Acad. Sci. GSSR, v. 90, n. 2, 1978
(in Russian).
[38]. Affine diameters of convex bodies, Bull. Acad. Sci. GSSR, v. 90, n. 3,
1978 (in Russian).
[39]. On an invariant defined for the class of three-dimensional polyhedra,
Bull. Acad. Sci. GSSR, v. 91, n. 1, 1978 (in Russian).
[40]. On the number of metrically transitive measures defined on the given
σ-algebra, Bull. Acad. Sci. GSSR, v. 92, n. 1, 1978 (in Russian).
[41]. Invariant measures in vector spaces, Bull. Acad. Sci. GSSR, v. 92, n.
2, 1978 (in Russian).
[42]. On the Banach-Tarski paradox, Bull. Acad. Sci. GSSR, v. 92, n. 3,
1978 (in Russian).
[43]. Sets having the uniqueness property with respect to the Lebesgue measure,
DAN SSSR, v. 240, n. 6, 1978 (in Russian).
[44]. On equidecomposability of three-dimensional polyhedra with respect to
the group of parallel translations and central symmetries, DAN SSSR, v. 243,
n. 6, 1978 (in Russian).
[45]. On the index of an isometric embedding, Proceedings of Institute of
Applied Mathematics TGU, 5 - 6, Tbilisi, 1978 (in Russian).
*[46]. Some Questions of Set Theory and Measure Theory, Izd. Tbil. Gos.
Univ., Tbilisi, 1978 (in Russian).
*[47]. Selected Topics in the Geometry of Euclidean Spaces, Izd. Tbil. Gos.
Univ., Tbilisi, 1978 (in Russian).
1979
[48]. The axiom of choice in the general system theory, Bull. Acad. Sci.
GSSR, v. 94, n. 3, 1979 (in Russian).
*[49]. Some Questions of Functional Analysis and their Applications, Izd.
Tbil. Gos. Univ., Tbilisi, 1979 (in Russian).
[50]. On a property of Hamel bases, Bull. Acad. Sci. GSSR, v. 95, n. 2,
1979 (in Russian).
[51]. The Szpilrajn-Marczewski axiom for extensions of Lebesgue measure,
Bull. Acad. Sci. GSSR, v. 96, n. 1, 1979 (in Russian).
3

[52]. On a covering of the continuum, Bull. Acad. Sci. GSSR, v. 96, n. 2,
1979 (in Russian).
1980
[53]. Absolutely nonmeasurable sets in abelian groups, Bull. Acad. Sci.
GSSR, v. 97, n. 3, 1980 (in Russian).
[54]. On the uniqueness property of a measure on its domain of definition,
Bull. Acad. Sci. GSSR, v. 99, n. 1, 1980 (in Russian).
[55]. On a class of subsets of the Euclidean plane having the uniqueness
property with respect to the Lebesgue measure, Bull. Acad. Sci. GSSR, v. 100,
n. 2, 1980 (in Russian).
[56]. Some questions of the theory of invariant measures, Bull. Acad. Sci.
GSSR, v. 100, n. 3, 1980 (in Russian).
[57]. Nonmeasurable Hamel bases, DAN SSSR, v. 253, n. 5, 1980 (in Russian).
[58]. On an application of the Banach theorem, Reports of the Seminar of
Institute of Applied Mathematics TGU, v. 14, 1980 (in Russian).
1981
[59]. Generalized limits on the real line, Bull. Acad. Sci. GSSR, v. 101, n.
1, 1981 (in Russian).
[60]. On Invariant Extensions of the Lebesgue Measure, Thesis, IM AN
USSR, Kiev, 1981 (in Russian).
*[61]. Elements of the Combinatorial Theory of Infinite Sets, Izd. Tbil. Gos.
Univ., Tbilisi, 1981 (in Russian).
[62]. On quasi-invariant measures, Bull. Acad. Sci. GSSR, v. 101, n. 3,
1981 (in Russian).
[63]. On a property of families of convex sets, Bull. Acad. Sci. GSSR, v.
102, n. 1, 1981 (in Russian).
[64]. Some properties of G-measures in Euclidean spaces, Bull. Acad. Sci.
GSSR, v. 102, n. 3, 1981 (in Russian).
[65]. To the theory of equidecomposability, Bull. Acad. Sci. GSSR, v. 103,
n. 3, 1981 (in Russian).
[66]. One application of the Baire property, Bull. Acad. Sci. GSSR, v. 104,
n. 2, 1981 (in Russian).
[67]. The absolute negligibility of compacts in infinite-dimensional Banach
spaces, Bull. Acad. Sci. GSSR, v. 104, n. 3, 1981 (in Russian).
1982
[68]. The absolute nonmeasurability of the unit ball in an infinite-dimensional
separable Hilbert space, Bull. Acad. Sci. GSSR, v. 107, n. 1, 1982 (in Russian).
[69]. Quasiinvariant measures in topological groups, Bull. Acad. Sci. GSSR,
v. 108, n. 2, 1982 (in Russian).
4

[70]. To the general theory of volumes, Bull. Acad. Sci. GSSR, v. 108, n.
3, 1982 (in Russian).
1983
*[71]. Invariant Extensions of the Lebesgue Measure, Izd. Tbil. Gos. Univ.,
Tbilisi, 1983, (in Russian).
[72]. The continuum hypothesis and some questions of measure theory, Bull.
Acad. Sci. GSSR, v. 111, n. 1, 1983 (in Russian).
[73]. On Borel measures in nonseparable metric spaces, Ukrain. Math.
Journ., v. 35, n. 5, 1983 (in Russian, with V.V.Buldygin, was translated into
English).
[74]. On measurable cardinals and the uniqueness property for σ-finite measures,
Bull. Acad. Sci. GSSR, v. 112, n. 1, 1983 (in Russian).
[75]. The Baire property and generalized derivatives, Bull. Acad. Sci. GSSR,
v. 112, n. 2, 1983 (in Russian).
[76]. An approach to some undecidable statements of set theory, Bull. Acad.
Sci. GSSR, v. 112, n. 3, 1983 (in Russian).
1984
*[77]. Topological Aspects of Measure Theory, Izd. Naukova Dumka, Kiev,
1984 (in Russian).
[78]. On quasi-invariant and invariant measures, Bull. Acad. Sci. GSSR, v.
113, n. 2, 1984 (in Russian).
[79]. On invariant measures in a Hilbert space, Bull. Acad. Sci. GSSR, v.
114, n. 1, 1984 (in Russian).
[80]. To the existence of quasi-invariant measures, Bull. Acad. Sci. GSSR,
v. 115, n. 1, 1984 (in Russian).
[81]. Groups of transformations and absolutely negligible sets, Bull. Acad.
Sci. GSSR, v. 115, n. 3, 1984 (in Russian).
[82]. On simple polyhedra, Reports of Seminar of Institute of Applied Mathematics
TGU, v. 18, Tbilisi, 1984 (in Russian).
[83]. To the uniqueness property of the Haar measure, Reports of Seminar
of Institute of Applied Mathematics TGU, v. 18, Tbilisi, 1984 (in Russian).
[84]. Independent families and universal coloured graphs, Reports of Seminar
of Institute of Applied Mathematics TGU, v. 18, Tbilisi, 1984 (in Russian).
1985
[85]. On some σ-algebras, Ukrain. Mathem. Journ., v. 37, n. 2, 1985 (in
Russian).
*[86]. Introduction to Combinatorial Geometry, Izd. Tbil. Gos. Univ.,
Tbilisi, 1985 (in Russian).
[87]. On a problem of combinatorial geometry, Bull. Acad. Sci. GSSR, v.
118, n. 1, 1985 (in Russian).
5

[88]. Partition of the three-dimensional space into congruent circles, Bull.
Acad. Sci. GSSR, v. 119, n. 1, 1985 (in Russian).
*[89]. Brunn-Minkowski Inequality and its Applications, Izd. Naukova Dumka,
Kiev, 1985 (in Russian, with V.V.Buldygin, a revised and expanded version of
this book was translated into English).
[90]. Coloured quasihomogeneous graphs, Bull. Acad. Sci. GSSR, v. 120, n.
2, 1985 (in Russian).
1986
[91]. Anderson’s inequality and unimodal measures, Prob. Theory and Math.
Stat., v. 35, Kiev, 1986 (in Russian, with V.V.Buldygin, was translated into
English).
[92]. On cylindrical and Borel σ-algebras, Ukrain. Math. Journ., v. 38, n.
1, 1986 (in Russian, with V.V.Buldygin, was translated into English).
[93]. On Baire spaces, Bull. Acad. Sci. GSSR, v. 123, n. 2, 1986 (in
Russian).
[94]. Quasipolygons and their uncountable unions, Bull. Acad. Sci. GSSR,
v. 124, n. 3, 1986 (in Russian).
1987
[95]. Some properties of isodyne topological spaces, Bull. Acad. Sci. GSSR,
v. 127, n. 2, 1987 (in Russian).
[96]. On some problems of combinatorial geometry, Proceedings of Tbilisi
Mathem. Inst. of A.M.Razmadze, v. 85, Tbilisi, 1987.
[97]. On Borel mappings of metric spaces, Bull. Acad. Sci. GSSR, v. 127,
n. 3, 1987 (in Russian).
1988
[98]. On some properties of Jordan curves, Bull. Acad. Sci. GSSR, v. 129,
n. 1, 1988 (in Russian).
[99]. Groups of motions and the uniqueness property of Lebesgue measure,
Bull. Acad. Sci. GSSR, v. 130, n. 1, 1988 (in Russian).
[100]. Realizations of graphs in the three-dimensional Euclidean space, Abstracts
of the IX-th Soviet Union Conference in Geometry, Kishinev, 1988.
[101]. On Borel measures in the space R α , Ukrain. Mathem. Journ., v. 40,
n. 5, 1988 (in Russian, was translated into English).
[102]. On perfect probability measures, Bull. Acad. Sci. GSSR, v. 131, n. 1,
1988 (in Russian).
[103]. ɛ-shifts and realizations of graphs, Bull. Acad. Sci. GSSR, v. 131, n.
2, 1988 (in Russian).
1989
6

[104]. Borel mappings of totally imperfect sets, Bull. Acad. Sci. GSSR, v.
133, n. 3, 1989 (in Russian).
[105]. The Baire property and nonmeasurable sets, Bull. Acad. Sci. GSSR,
v. 134, n. 3, 1989 (in Russian).
[106]. On negligible sets, Math. Inst. Univers. of Wroclaw, Preprint n. 106,
Wroclaw, 1989.
*[107]. Applications of Set Theory, Izd. Tbil. Gos. Univ., Tbilisi, 1989 (in
Russian).
[108]. To the existence of statistical estimates for strongly separative families
of probability measures, Proceedings of Tbilisi Mathem. Inst. of A.M.Razmadze,
v. 92, Tbilisi, 1989.
[109]. An application of the Kuratowski-Ulam theorem, Bull. Acad. Sci.
GSSR, v. 134, n. 3, part 2, 1989 (in Russian).
[110]. Borel measures in metric spaces, Bull. Acad. Sci. GSSR, v. 135, n.
1, 1989 (in Russian).
[111]. On some problems of set theory, Bull. Acad. Sci. GSSR, v. 135, n.
2, 1989 (in Russian).
[112]. On negligible sets, Bull. Acad. Sci. GSSR, v. 136, n. 1, 1989 (in
Russian).
1990
[113]. On cardinalities of isodyne topological spaces, Bull. Acad. Sci. GSSR,
v. 137, n. 1, 1990 (in Russian).
[114]. Martin’s axiom and Γ-selectors, Bull. Acad. Sci. GSSR, v. 137, n. 2,
1990 (in Russian).
[115]. On some problems connected with Lebesgue measure and Baire property,
Bull. Acad. Sci. GSSR, v. 137, n. 3, 1990 (in Russian).
[116]. Luzin spaces and Bernstein sets, Bull. Acad. Sci. GSSR, v. 138, n.
1, 1990 (in Russian).
*[117]. Selected Topics in General Topology, Izd. Tbil. Gos. Univ., Tbilisi,
1990 (in Russian).
[118]. On the existence of sets without the Baire property, Bull. Acad. Sci.
GSSR, v. 138, n. 3, 1990 (in Russian).
[119]. On a problem of uniformization of sets, Bull. Acad. Sci. GSSR, v.
140, n. 2, 1990 (in Russian).
1991
*[120]. Vitali’s Theorem and its Generalizations, Izd. Tbil. Gos. Univ.,
Tbilisi, 1991, (in Russian).
[121]. On some topological realizations of infinite graphs, Bull. Acad. Sci.
Georgia, v. 142, n. 3, 1991 (in Russian).
[122]. On the Baire property and bases of ideals of first category sets, Bull.
Acad. Sci. Georgia, v. 143, n. 2, 1991 (in Russian).
7

[123]. Some problems in measure theory, Colloq. Mathem., v. 62, 1991.
[124]. On selectors associated with some subgroups of the real line, Bull.
Acad. Sci. Georgia, v. 144, n. 2, 1991 (with J.Cichon and B.Weglorz).
[125]. A note on Luzin sets and Sierpinski sets, Bull. Acad. Sci. Georgia,
v. 143, n. 3, 1991 (in Russian).
1992
[126]. Problems and Examples from Elementary Mathematics, Tbilisi, 1992
(in Georgian, co-authors: G.Jaiani and others).
[127]. On translations of measurable sets and of sets with the Baire property,
Bull. Acad. Sci. Georgia, v. 145, n. 1, 1992 (in Russian, with W.Wilczyński).
*[128]. Baire Property and its Applications, Proceedings of I.N.Vekua Institute
of Applied Mathematics, vol. 43, 1992, 120 pp. (in Russian).
1993
[129]. Measurable spaces with ideals and selectors, Bull. Acad. Sci. Georgia,
v. 147, n. 1, 1993 (in Russian).
[130]. On sets of Vitali’s type, Proc. Amer. Math. Soc., v. 118, n. 4, 1993,
1221–1228 (with J.Cichoń and B.Weglorz).
[131]. On the sections of analytic sets, Bull. Acad. Sci. Georgia, v. 147, n.
2, 1993, 223–226 (in Russian).
[132]. Γ-topology and the Baire property, Bull. Acad. Sci. Georgia, v. 148,
n. 1, 1993 (in Russian).
1994
[133]. Small sets with respect to certain classes of topologies, Colloq. Mathem.
v. LXVII, n. 1, 1994, 123–129.
[134]. On nonseparable invariant measures with the uniqueness property,
Bull. Acad. Sci. Georgia, v. 149, n. 1, 1994 (in Russian).
[135]. On the principle of condensation of singularities, Bull. Acad. Sci.
Georgia, v. 149, n. 2, 1994 (in Russian).
[136]. Some remarks on density points and the uniqueness property for invariant
extensions of the Lebesgue measure, Acta Universitatis Carolinae - Mathematica
et Physica, vol. 35, no. 2, 1994, pp. 33 - 39.
[137]. Generalized Sierpinski sets, Georgian Mathematical Journal, vol. 1,
no. 5, 1994, pp. 479-486.
1995
[138]. Some questions concerning invariant extensions of Lebesgue measure,
Real Analysis Exchange, vol. 20, no. 2, 1994–1995, pp. 580–592.
[139]. On separable supports of Borel measures, Georgian Mathematical
Journal, vol. 2, no. 1, 1995, pp. 45 - 53.
8

*[140]. Subsets of the Real Line, Part 1, ̷Lódź University Press, ̷Lódź, 1995,
(with J.Cichoń and B.Weglorz).
[141]. Some remarks on the property (N) of Luzin, Annales Mathematicae
Silesianae, 9, 1995, pp. 33–41.
[142]. Some remarks on nonmeasurable almost invariant sets, Folia Mathematica,
̷Lódź, 7, 1995, pp. 41–50.
[143]. Small sets in uncountable abelian groups, Folia Mathematica, ̷Lódź,
7, 1995, pp. 31–39.
[144]. On density topologies generated by ideals, Folia Mathematica, ̷Lódź,
7, 1995, pp. 51–62, (with J.Hejduk).
[145]. On translations of sets and functions, Journal of Applied Analysis, 1,
n. 2, 1995, 145–158.
1996
[146]. On density points with respect to von Neumann’s topology, Real Analysis
Exchange, vol. 21, no. 1, 1995–1996 (with J.Hejduk).
[147]. Some remarks on additive properties of invariant σ-ideals on the real
line, Real Analysis Exchange, vol. 21, no. 2, 1995–1996.
[148]. On the Steinhaus property for invariant measures, Real Analysis Exchange,
vol. 21, no. 2, 1995–1996.
[149]. Some partitions consisting of Jordan curves, Georgian Mathematical
Journal, vol. 3, no. 3, 1996, pp. 233 - 238.
[150]. A note on the Sierpiński partition, Journal of Applied Analysis, vol.
2, no. 1, 1996, pp. 41 - 48.
[151]. On nonmeasurable subgroups of the real line, Journal of Applied Analysis,
vol. 2, no. 2, 1996, pp. 171 - 181.
*[152]. Selected Topics of Point Set Theory, ̷Lódź University Press, ̷Lódź,
1996.
1997
[153]. On almost rigid mathematical structures, Folia Mathematica, ̷Lódź,
9, 1997, pp. 41–58.
[154]. On Vitali construction for commutative groups with quasiinvariant
measures, Folia Mathematica, ̷Lódź, 9, 1997, pp. 59–69.
[155]. On almost invariant subsets of the real line, Folia Mathematica, ̷Lódź,
9, 1997, pp. 27–39.
[156]. On selectors nonmeasurable with respect to quasi-invariant measures,
Real Analysis Exchange, vol. 22, no. 1, 1996 - 1997.
[157]. On some subsets of spaces equipped with transformation groups, Real
Analysis Exchange, vol. 22, no. 2, 1996 - 1997.
[158]. On the uniqueness of Lebesgue and Borel measures, Journal of Applied
Analysis, vol. 3, no. 1, 1997.
9

[159]. Sup-measurable and weakly sup-measurable mappings in the theory of
ordinary differential equations, Journal of Applied Analysis, vol. 3, no. 2, 1997.
1998
[160]. On countably generated invariant σ-algebras which do not admit measure
type functionals, Real Analysis Exchange, vol. 23, no. 1, 1997 - 1998.
*[161]. Applications of Point Set Theory in Real Analysis, Kluwer Academic
Publishers, Dordrecht, 1998, 244 pp.
*[162]. Transformation Groups and Invariant Measures: Set-Theoretical Aspects,
World Scientific Publishing Co., Singapore, 1998, 260 p.
1999
[163]. On uncountable unions and intersections of measurable sets, Georgian
Mathematical Journal, vol. 6, no. 3, 1999, pp. 201 - 212 (co-author M.
Balcerzak).
[164]. On Vitali’s theorem for groups of motions of Euclidean space, Georgian
Mathematical Journal, vol. 6, no. 4, 1999, pp. 323 - 334.
[165]. Subsets of the plane with small linear sections and invariant extensions
of the two-dimensional Lebesgue measure, Georgian Mathematical Journal, vol.
6, no. 5, 1999, pp. 441 - 446.
[166]. Some remarks on quasiinvariant and invariant measures, Real Analysis
Exchange, vol. 24, no. 1, 1998 - 1999, pp. 427 - 434.
[167]. On C-points of compact sets in locally convex spaces, Soochow Journal
of Mathematics, vol. 25, no. 4, 1999, pp. 401 - 410.
[168]. Absolute continuity of measures, Ver. i Mat. Stat., Moscow, 1999 (in
Russian).
[169]. Additive set function, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[170]. Sigma-algebra of sets, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[171]. Borel function, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[172]. Borel set, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[173]. Completely additive set function, Ver. i Mat. Stat., Moscow, 1999 (in
Russian).
[174]. Signed measure, Ver. i Mat. Stat., Moscow, 1999 (in Russian, coauthor:
A.A. Borovkov).
[175]. Measurable function, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[176]. Sigma-measurable function, Ver. i Mat. Stat., 1999 (in Russian).
[177]. Kolmogorov theorem on finite-dimensional distributions, Ver. i Mat.
Stat., Moscow, 1999 (in Russian).
[178]. Finitely additive set function, Ver. i Mat. Stat., Moscow, 1999 (in
Russian).
[179]. Measure, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[180]. Monotone class of sets, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[181]. Extension of measures, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
10

[182]. Projective systems of measures, Ver. i Mat. Stat., 1999 (in Russian).
[183]. Product measure, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[184]. Measure space, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[185]. Prokhorov criterion, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[186]. Radon-Nikodym theorem, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[187]. Singular component of a measure, Ver. i Mat. Stat., Moscow, 1999
(in Russian).
[188]. Singularity of measures, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[189]. Countably additive set function, Ver. i Mat. Stat., Moscow, 1999 (in
Russian).
[190]. Hahn theorem on a signed measure, Ver. i Mat. Stat., Moscow, 1999
(in Russian).
[191]. Cylindrical sigma-algebra, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[192]. Equivalent measures, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
[193]. Elementary measure, Ver. i Mat. Stat., Moscow, 1999 (in Russian).
2000
*[194]. Strange Functions in Real Analysis, Marcel Dekker, Inc., New York,
2000.
*[195]. Geometric Aspects of Probability Theory and Mathematical Statistics,
Kluwer Academic Publishers, Dordrecht, 2000 (co-author V.V. Buldygin).
[196]. A Collection of Problems in Elementary Mathematics, (co-authors:
T.Sajeniuk, T.Korshia, T.Djangveladze), Tbilisi, 2000 (in Georgian).
[197]. On analogues of some classical subsets of the real line, Journal of
Applied Analysis, vol. 6, no. 1, 2000, pp. 77 - 85.
[198]. Invariant measurable structures on groups and nonmeasurable subgroups,
Real Analysis Exchange, vol. 25, no.2, 1999 - 2000, pp. 931 - 936.
[199]. On measurability properties of subgroups of a given group, Real Analysis
Exchange, 24-th Summer Symposium Conference Reports, May 2000, pp.
143 - 145.
2001
[200]. On the existence of nonmeasurable subgroups of commutative groups,
Real Analysis Exchange, vol. 27, no. 1, 2001 - 2002.
[201]. On vector sums of measure zero sets, Georgian Mathematical Journal,
vol. 8, no. 3, 2001, pp.493 - 498.
[202]. Geometric aspects of the principle of a decreasing sequence of segments,
Physics and Mathematics at School, vol. 117, 2001, pp. 67 - 71 (in
Georgian).
11

[203]. The first Georgian mathematical olympiad in the XXI-th century, (coauthors:
T.Djangveladze, N.Mchedlishvili, A.Kirtadze), Tbilisi, 2001, pp. 150
(in Georgian).
2002
[204]. On measurability properties connected with the superposition operator,
Real Analysis Exchange, vol. 28, no. 1, 2002 - 2003, pp. 205-214.
[205]. On the uniqueness property for products of symmetric invariant probability
measures, Georgian Mathematical Journal, vol. 9, no. 1, 2002, pp. 75 -
82.
[206]. A note on convexly independent subsets of an infinite set of points,
Georgian Mathematical Journal, vol. 9, no. 2, 2002, pp. 303 - 307.
[207]. On ideals with projective bases, (co-author: J.Cichoń), Georgian Mathematical
Journal, vol. 9, no. 3, 2002, pp 461 - 472.
[208]. The final of the pupils mathematical olympiad (2001-2002 academic
year), (co-author: T.Djangveladze), Physics and Mathematics at School, vol.
118, 2002.
2003
[209]. On maximal ot-subsets of the Euclidean plane, Georgian Mathematical
Journal, vol. 10, no. 1, 2003, pp. 127 - 131.
[210]. Extending quasi-invariant measures by using subgroups of a given
group, Georgian Mathematical Journal, vol. 10, no. 2, 2003, pp. 247 - 255.
[211]. On faces of convex polyhedra in R 3 with a small number of sides,
Georgian Mathematical Journal, vol. 10, no. 4, 2003.
[212]. Some applications of graph theory, Bulletin of TICMI, vol. 7, 2003,
pp. 31 - 32.
2004
[213]. On homogeneous coverings of Euclidean spaces, Georgian Mathematical
Journal, vol. 11, no. 1, 2004, pp. 105 - 109.
[214]. Homogeneous coverings of the plane by circumferences, Physics and
Mathematics at School, vol. 120, 2004, pp. 47 - 50 (in Georgian).
[215]. On absolutely nonmeasurable additive functions, Georgian Mathematical
Journal, vol. 11, no. 2, 2004, pp. 301 - 306.
*[216]. Nonmeasurable Sets and Functions, North-Holland Mathematics
Studies, Elsevier Publishing Co., Amsterdam, 2004, 330 p.
[217]. On negligible and absolutely nonmeasurable subsets of the Euclidean
plane, Georgian Mathematical Journal, vol. 11, no. 3, 2004.
[218]. On algebraic sums of measure zero sets in uncountable commutative
groups, Proc. A. Razmadze Math. Institute, vol. 135, 2004, pp. 97 - 103
(co-author: A. Kirtadze).
12

[219]. On algebraic sums of absolutely negligible sets, Proc. A. Razmadze
Math. Insitute, vol. 136, 2004, pp. 55 - 61 (co-author: A.Kirtadze).
[220]. On the measurability of functions with respect to certain classes of
measures, Georgian Mathematical Journal, vol. 11, no. 3, 2004, pp. 489 - 494
(co-author: A.Kirtadze).
[221]. On generalized step-functions and superposition operators, Georgian
Mathematical Journal, vol. 11, no. 4, 2004, pp. 753 - 758.
2005
[222]. On absolutely negligible sets in uncountable solvable groups, Georgian
Mathematical Journal, vol. 12, no. 2, 2005.
[223]. The algebraic sum of two absolutely negligible sets can be an absolutely
nonmeasurable set, Georgian Mathematical Journal, vol. 12, no. 3, 2005, pp.
[224]. On discrete mathematics, Physics and Mathematics at School, vol.
121, 2005, pp. 58-64 (in Georgian, co-author A. Kipiani).
[225]. On mutually coherent enumerations of countable sets, Georgian Mathematical
Journal, vol. 12, no. 4, 2005, pp. 671 - 678.
[226]. Nonmeasurable vector sums of measure zero sets, International Conference:
Modern Problems and New Trends in Probability Theory, Abstracts,
Chernivtsi, Ukraine, June 19 - 26, 2005, pp. 121 - 122.
[227]. Nonseparable left-invariant measures on uncountable solvable groups,
Proc. A.Razmadze Math. Institute, vol. 139, 2005 (co-author A. Kirtadze).
2006
*[228]. Strange Functions in Real Analysis, Second Edition, Chapman and
Hall/CRC, Taylor & Francis Books, Boca Raton - New York - London -Singapore,
2006, 430 p.
[229]. On some mutual positions of hyperplanes in a finite-dimensional affine
space, Georgian Mathematical Journal, vol. 13, no. 1, 2006.
[230]. On additive absolutely nonmeasurable Sierpinski-Zygmund functions,
Real Analysis Exchange, vol. 31, no. 2, 2005-2006.
[231]. On measurable Sierpinski-Zygmund functions, Journal of Applied
Analysis, vol. 12, no. 2, 2006, pp. 283-292.
[232]. On decompositions of a cube into cubes and simplexes, Georgian Mathematical
Journal, vol. 13, no. 2, 2006.
2007
[233]. On the measurability of additive functionals, Georgian Mathematical
Journal, vol. 14, no. 1, 2007, pp. 135-143.
[234]. On weakly metrically transitive measures and nonmeasurable sets, Real
Analysis Exchange, vol. 32, no. 2, 2007, pp. 553-562. (co-author A. Kirtadze).
[235]. On nonmeasurable subgroups of uncountable solvable groups, Georgian
Mathematical Journal, vol. 14, no. 3, 2007 (co-author A. Kirtadze).
13

[236]. On extensions of partial functions, Expositiones Mathematicae, vol.
25, issue 4, 2007, pp. 345-353 (co-author A. Kirtadze).
[237]. Some aspects of the measure extension problem, Proc. A. Razmadze
Math. Inst., vol. 143, 2007, pp. 73-78.
[238]. The absolute nonmeasurability of Minkowski’s sum of certain universal
measure zero sets in a topological vector space, International Conference:
Skorokhod Space. 50 Years On; Abstracts, Kiev, Ukraine, June 17-23, 2007.
*[239]. Mathematical Sketches, Part 1, I. Chavchavadze State University
Press, Tbilisi, 2007 (in Georgian).
[240]. Ergodic components and nonseparable extensions of invariant measures,
Proc. A. Razmadze Math. Institute, vol. 145, 2007.
[241]. Some combinatorial properties of finite line-systems in the Euclidean
plane, Georgian Mathematical Journal, vol. 14, no. 4, 2007.
2008
[242]. On measurability of algebraic sums of small sets, Studia Scientiarum
Mathematicarum Hungarica, vol. 45, no. 3, 2008 (co-author A. Kirtadze).
[243]. A nonseparable extension of the Lebesgue measure without new nullsets,
Real Analysis Exchange, vol. 33, no. 1, 2008.
[244]. On absolutely nonmeasurable sets and functions, Georgian Mathematical
Journal, vol. 15, no. 2, 2008, pp. 317-325.
[245]. Combinatorial properties of families of sets and Euler-Venn diagrams,
Proc. A. Razmadze Math. Inst., vol. 146, 2008 (co-author T. Tetunashvili).
[246]. On bad descriptive structure of Minkowski’s sum of certain small sets
in a topological vector space, Theory of Stochastic Processes, vol. 14 (30), issue
2, 2008.
[247]. On some families of convex functions, Workshop: Variable Exponent
Analysis and Related Topics, 2-5 September, 2008, Tbilisi, Georgia
http://haota.ualg.pt/vea/workshops.html
[248]. On some combinatorial problems concerning geometrical realizations
of finite and infinite families of sets, Georgian Mathematical Journal, vol. 15,
no. 4, 2008, pp. 665-675 (co-author T. Tetunashvili).
*[249]. The Beginnings of Set Theory, Part 1, I. Chavchavadze State University
Press, Tbilisi, 2008 (in Georgian).
[250]. Some properties of step-functions connected with extensions of measures,
Acta Universitatis Carolinae, Phys.-Math. Series, v. 49, n. 2, 2008.
2009
[251]. Metrical transitivity and nonseparable extensions of invariant measures,
Taiwanese Journal of Mathematics, vol. 13, no. 3, 2009.
[252]. On sums of real-valued functions with extremely thick graphs, Expositiones
Mathematicae, vol. 27, no. 2, 2009, pp. 161-169.
14

[253]. Almost measurable real-valued functions and extensions of the Lebesgue
measure, Proc. A. Razmadze Math. Institute, vol. 150, 2009, pp. 135-138.
[254]. On nonmeasurable functions of two variables and iterated integrals,
Georgian Mathematical Journal, v. 16, n. 4, 2009.
[255]. On the existence of σ-finite non-separable invariant measures on uncountable
groups, International Conference: Stochastic Analysis and Random
Dynamics, Abstracts, June 14-20, 2009, Lviv, Ukraine.
[256]. On thick subgroups of uncountable σ-compact locally compact commutative
groups, Topology and its Applications, vol. 156, issue 14, 2009, pp.
2364-2369.
[257]. Finite families of negligible sets and invariant extensions of the Lebesgue
measure, Proc. A. Razmadze Math. Inst., vol. 151, 2009, pp. 119-123.
[258]. On sets with homogeneous linear sections, Proc. A. Razmadze Math.
Institute, vol. 151, 2009, pp. 124-128.
*[259]. Topics in Measure Theory and Real Analysis, Atlantis Press and
World Scientific, Amsterdam-Paris, 2009, 470 p.
[260]. On some applications of set-theoretical methods in Euclidean geometry,
Bulletin of TICMI, v. 13, 2009.
2010
[261]. On some coverings of the Euclidean plane with pairwise congruent
circles, Amer. Math. Monthly, v. 117, n. 5, 2010, (co-author: T. Sh. Tetunashvili).
[262]. On almost measurable real-valued functions, Studia Scientiarum Mathematicarum
Hungarica, v. 47, n. 2, 2010, pp. 257-266.
[263]. Piecewise affine approximations of continuous functions of several
variables and Gale polyhedra, Proc. A. Razmadze Math. Institute, v. 152,
2010.
[264]. On nonmeasurable unions of measure zero sections of plane sets, Proc.
A. Razmadze Math. Inst., v. 154, 2010.
[265]. On a relationship between the measurability and continuity of realvalued
functions, Georgian Mathematical Journal, v. 17, n. 4, 2010.
*[266]. Mathematical Sketches, part 2, Ilia State University Press, Tbilisi,
2010 (in Georgian).
[267]. On non-elementary methods in elementary geometry, Journal of Geometry,
v. 97, numbers 1-2, 2010.
[268]. Some combinatorial problems on the measurability of functions with
respect to invariant extensions of the Lebesgue measure, Acta Universitatis Carolinae,
Phys.-Math. Ser., v. 51, 2010, pp. 57-65.
2011
[269]. A combinatorial problem on translation-invariant extensions of the
Lebesgue measure, Expositiones Mathematicae, v. 29, n. 1, 2011, pp. 150-158.
15

[270]. Measurability properties of Vitali sets, Amer. Math. Monthly, v. 118,
n. 10, 2011, pp. 693-703.
[271]. Some discrete geometric structures and associated algorithms, Proc.
A. Razmadze Mathematical Institute, v. 155, 2011, pp. 142-148.
[272]. On ordinary differential equations with bad right-hand sides, Proc. A.
Razmadze Mathematical Institute, v. 155, 2011, pp. 139-141.
[273]. On a relationship between absolutely nonmeasurable functions and
Sierpiński-Zygmund functions, Georgian Mathematical Journal, v. 18, n. 2,
2011.
[274]. A note on algebraic convex curves of constant width, Georgian Mathematical
Journal, v. 18, n. 4, 2011.
[275]. Some remarks concerning monotone and continuous restrictions of
real-valued functions, Proc. A. Razmadze Mathematical Institute, v. 157, 2011,
pp. 11-21.
[276]. On finite and infinite ot-sets, Bulletin of TICMI, v. 15, 2011, pp.
27-34.
2012
[277]. Measurable and nonmeasurable sets with homogeneous sections, Georgian
Mathematical Journal, v. 19, n. 2, 2012, pp. 247-258.
*[278]. The Beginnings of Set Theory, Part 2, Tbilisi, 2012 (in Georgian).
[279]. A large group of absolutely nonmeasurable additive functions, Real
Analysis Exchange, v. 37, n. 2, 2011-2012, pp. 467-476.
[280]. Some properties of at-sets and ot-sets in a Hilbert space, Proceedings
of A. Razmadze Mathematical Institute, v. 159, 2012, pp. 151-155.
[281]. On some topologic-geometrical properties of external bisectors of a
triangle, Georgian Mathematical Journal, v. 19, n. 4, 2012, pp. 697-704.
[282]. Ergodic measures and the definability of subgroups via normal extensions
of such measures, Theory of Stochastic Processes, v. 18 (34), n. 1, 2012,
pp. 58-64.
[283]. Some geometric consequences of Ramsey’s combinatorial theorem,
Bulletin of TICMI, v. 16, n. 1, 2012, pp. 34-42.
16

Citation of some works of A.B. Kharazishvili
Remark. The symbol (*) marks monographs, textbooks, handbooks, surveys,
theses, or lecture courses.
1975
G. Nijaradze, Density points and invariant sigma-finite measures, Bull. Acad.
Sci. GSSR, vol. 80, no.1, 1975 (in Russian).
[13].
G. Nijaradze, On some properties of measures which are invariant with respect
to discrete groups of motions, Bull. Acad. Sci. GSSR, vol. 80, no. 2, 1975
(in Russian).
[6], [11].
G. Nijaradze, On the stability property of sets with respect to small shifts,
Bull. Acad. Sci. GSSR, vol. 80, no.3, 1975 (in Russian).
[13], [14].
1976
H. Guggenheimer, E.Lutwak, Characterization of n-dimensional parallelotope,
Amer. Math. Monthly, vol. 83, no. 6, 1976.
[4].
G. Nijaradze, On some properties of sigma-finite measures given on Euclidean
spaces, Bull. Acad. Sci. GSSR, v. 83, n. 3, 1976 (in Russian).
[17].
G. Nijaradze, On nonmeasurable subsets of Euclidean spaces, Proceedings of
the Conference of Young Scientists in Mathematics and Mechanics, Tbilisi State
University Press, Tbilisi, 1976 (in Russian).
[17].
1977
P. Gruber, Über den Durchschnitt einen abnehmenden Folge von Parallelepipeden,
Elemente der Mathematik, v. 32, n. 1, 1977.
[4].
1

1978
(*) V. Boltyanskii, P.Soltan, Combinatorial Geometry of Various Classes of
Convex Sets, Acad. Nauk Mold. SSR, ”Stinitsa”, Kishinev, 1978, 300 p. (in
Russian).
[3], [4].
G. Nijaradze, On regular systems which are not Vitali ones, Bull. Acad. Sci.
GSSR, v. 90, n. 2, 1978 (in Russian).
[13], [19].
1979
A. Kipiani, On countable equidecomposability of sets in abstract spaces, Bull.
Acad. Sci. GSSR, v. 95, n. 2, 1979 (in Russian).
[42], [46].
1980
R. Tsakadze, On totally homogeneous spaces, Bull. Acad. Sci. GSSR, v. 98,
n. 1, 1980 (in Russian).
[46], [49].
A. Gabrichidze, On symmetric sets, Bull. Acad. Sci. GSSR, v. 100, n. 3,
1980 (in Russian).
[25], [47].
1981
(*) V. Boltyanskii, Combinatorial Geometry, in the Series: ”Algebra, Topology,
Geometry”, v. 19, 1981, pp. 209 - 274 (in Russian).
[3], [34], [44].
(*) J. Böhm, E. Hertel, Polyedergeometrie in n-dimensionalen Räumen konstanter
Krümmung, Birkhauser, Basel-Boston-Stuttgart, 1981, 380 p.
[27], [29].
(*) Ch. Davis, B. Grünbaum, F.A. Sherk, The Geometric Vein, Springer-
Verlag, Berlin, 1981, 598 p.
[47].
1982
A. Pelc, Semiregular invariant measures on abelian groups, Proc. Amer.
Math. Soc., v. 86, 1982.
[15].
E. Hertel, Some generalizations of equidecomposability theory of polyhedra,
Forschungsergebnisse, Universitat Jena, N/82/49, 1982 (in Russian).
2

1983
[34].
(*) P. Gruber, J. Wills, Convexity and its Applications, Birkhauser, Basel,
1983.
[4].
1984
J. Burzyk, C. Klis, Z. Lipecki, On metrizable abelian groups, Coll. Math., v.
XLIX, 1984.
[53].
Z. Zerakidze, On weakly separated and separated families of probability measures,
Bull. Acad. Sci. GSSR, v. 113, n. 2, 1984 (in Russian).
[49].
A. Gabrichidze, One class of symmetric sets, Bull. Acad. Sci. GSSR, v.
114, n. 1, 1984 (in Russian).
[25], [47].
1985
(*) I. Rival, Graphs and Order, D. Reidel Publ. Co., University of California,
1985, 796 p.
[8].
K. Ciesielski, A. Pelc, Extensions of invariant measures on Euclidean spaces,
Fund. Math., v. 125, 1985.
[15], [46].
H. Kaiser, Mehrfach-orthogonale Simplexe in Räumen konstanter
Krümmung, Beitrage zur Algebra und Geometrie, v. 19, 1985.
[29].
G. Pantsulaia, On generalized integrals, Bull. Acad. Sci. GSSR, v. 117, n.
1, 1985 (in Russian).
[66].
R. Tsakadze, On the notion of absolute nonmeasurability, Bull. Acad. Sci.
GSSR, v. 118, n.1, 1985 (in Russian).
[64], [68].
R. Tsakadze, On absolutely negligible sets in Euclidean spaces, Bull. Acad.
Sci. GSSR, v. 118, n. 3, 1985 (in Russian).
[71], [77].
3

G. Pantsulaia, On the existence of a quasi-invariant measure on a non-locally
compact non-commutative topological group, Bull. Acad. Sci. GSSR, v. 120, n.
1, 1985 (in Russian).
[77], [79].
G. Pantsulaia, On some properties of families of probability measures, Bull.
Acad. Sci. GSSR, v. 120, n. 2, 1985 (in Russian).
[71].
G. Nijaradze, On regular systems for some invariant extensions of Lebesgue
measure, ”Topological Aspects of the Theory of Functions”, Tbil. State Univ.,
Tbilisi, 1985 (in Russian).
[71].
Z. Zerakidze, On consistent estimates in nonseparable metric spaces, ”Topological
Aspects of the Theory of Functions”, Tbil. State Univ., Tbilisi, 1985 (in
Russian).
[73].
R. Tsakadze, On absolutely nonmeasurable sets, ”Topological Aspects of the
Theory of Functions”, Tbil. State Univ., Tbilisi, 1985 (in Russian).
[77].
A. Kirtadze, To the question on the existence of a family of mutually singular
measures in the space R N , whose cardinality is maximal, ”Topological Aspects
of the Theory of Functions”, Tbil. State Univ., Tbilisi, 1985 (in Russian).
[71], [79].
G. Pantsulaia, On generalized integrals for vector-functions, ”Topological
Aspects of the Theory of Functions”, Tbil. State Univ., Tbilisi, 1985 (in Russian).
[66].
V. Tskhadaia, Quasi-invariant and invariant measures in topological spaces,
”Topological Aspects of the Theory of Functions”, Tbil. State University, Tbilisi,
1985 (in Russian).
[79].
A. Gabrichidze, On some questions of combinatorial geometry in finitedimensional
normed vector spaces, The First Soviet Conference in Combinatorial
Geometry, Batumi, 1985 (in Russian).
[47].
H. Kaiser, To the question on decomposability of simplices into k-orthogonal
simplices, The First Soviet Conference in Combinatorial Geometry, Batumi,
1985 (in Russian).
[29].
4

G. Nijaradze, On some properties of discrete groups of motions of Euclidean
spaces, The First Soviet Conference in Combinatorial Geometry, Batumi, 1985
(in Russian).
[71].
T. Sajeniuk, On partitions of R 3 into congruent convex curves, The First
Soviet Conference in Combinatorial Geometry, Batumi, 1985 (in Russian).
[88].
(*). N. Vakhania, V. Tarieladze, S. Chobanian, Probability Distributions in
Banach Spaces, ”Nauka”, Moscow, 1985, 550 p. (in Russian).
[61].
1986
(*) S. Kakutani, Selected Papers, vol. 2, Birkhäuser, Basel, 1986, 458 p.
[16].
I.I. Bajenov, To the Liapunov theorem on the range of a vector measure,
Optimization, Institute of Mathematics, SO AN SSSR, 1986 (in Russian).
[71].
(*) A. Pelc, Invariant measures on discrete groups, Dissertationes Mathematicae,
vol. CCLV, 1986.
[15], [31], [46], [49], [53].
M.G. Rozinas, Criterion of nonlinear homogeneity of plane figures, Izvestia
VUZ, Matematika, 1986 (in Russian).
[65].
G. Nijaradze, On some geometric properties of G-measures, Bull. Acad. Sci.
GSSR, v. 123, n. 2, 1986 (in Russian).
[64].
V. Tskhadaia, On absolutely negligible sets, Bull. Acad. Sci. GSSR, v. 123,
n. 3, 1986 (in Russian).
[46], [71], [77].
E. Hertel, Zerlegungsähnlichkeit von Polygonen, Elemente der Mathematik,
v. 41, 1986, pp. 139-143.
[34].
H. Kaiser, Zum Problem der Zerlegbarkeit von Simplexen in Orthoscheme,
Studia Scientiarum Mathematicarum Hungarica, v. 21, 1986, pp. 227-242.
[29].
1987
V.V. Buldygin, Convergence of Fourier series of stationary
5

Gaussian processes, Ukrain. Math. Journal, v. 39, n. 3, 1987 (in Russian).
[89].
G.A. Galperin, Solving Proizvolov’s problem of covering a multi dimensional
polyhedron with pyramids - generalizations of the problem, Dokl. Akad. Nauk
SSSR, v. 293, n. 2, 1987 (in Russian).
[86].
P. Zakrzewski, The existence of universal invariant semiregular measures on
groups, Proc. Amer. Math. Soc., vol. 99, 1987.
[15].
H. Kaizer, On a classification of n-dimensional simplices, Bull. Acad. Sci.
GSSR, v. 125, n. 1, 1987 (in Russian).
[29], [47].
A. Kirtadze, G. Pantsulaia, On essential uniqueness of invariant measures,
Bull. Acad. Sci. GSSR, v. 127, n. 1, 1987 (in Russian).
[71], [78], [79].
T. Sajeniuk, On combinatorial properties of nets in Euclidean spaces, Soviet
Geometry Conference in Honour of A.D. Alexandrov, Novosibirsk, 1987 (in
Russian).
[82].
T. Sajeniuk, On some inductive constructions in combinatorial geometry,
Proc. I.Vekua Inst. of Appl. Math., v. 20, 1987 (in Russian).
[82], [87], [88].
A. Kipiani, Product-isomorphisms of binary relations and some of their applications,
Proc. I.Vekua Inst. of Appl. Math., v. 20, 1987 (in Russian).
[28], [61].
G. Nijaradze, To the question on the existence of absolutely nonmeasurable
sets and the Vitali construction, Proc. I.Vekua Inst. of Appl. Math., v. 20,
1987 (in Russian).
[36], [64].
D. Bersenadze, The Suslin property for measures and the Carathéodory extension
theorem, Proc. I.Vekua Inst. of Appl. Math., v. 20, 1987 (in Russian).
[71].
G. Sokhadze, To the Dilworth theorem on decomposition of ordered sets,
Proc. I.Vekua Inst. of Appl. Math., v. 20, 1987 (in Russian).
[61].
G. Nijaradze, On some geometric topics in the theory of measures and volumes,
Proc. A.Razmadze Math. Inst., v. 85, 1987 (in Russian).
[71].
6

V. Pokrovskii, Decompositions of n-dimensional polyhedra and the Zylev-
Debrunner theorem, Proc. A.Razmadze Math. Inst., v. 85, 1987 (in Russian).
[34].
T. Sajeniuk, On combinatorial properties of subsets of the Euclidean plane,
Proc. A.Razmadze Math. Inst., v. 85, 1987 (in Russian).
[82], [87].
1988
P. Neumann, Homogeneity of infinite permutation groups, Bull. London
Math. Soc., v. 20, n. 4, 1988.
[10].
P. Zakrzewski, Extensions of invariant ideals, Algebra Univers., v. 25, n. 2,
1988.
[15].
P. Zakrzewski, On universal semiregular invariant measures, The Journal of
Symbolic Logic, v. 53, n. 4, 1988.
[15].
(*) A. Kusraev, S. Maliugin, Some Questions of the Theory of Vector Measures,
Inst. Math. SO AN SSSR, Novosibirsk, 1988, 200 p., (in Russian).
[77].
V. Soltan, Nguen Man Hung, To the problem of Grünbaum on affine diameters,
Bull. Acad. Sci. GSSR, v. 132, n. 1, 1988 (in Russian).
[38].
A. Kipiani, Some combinatorial problems connected with product
isomorphisms of binary relations, Acta Univ. Carolin., Ser. Math.-Phys., v.
29, n. 2, 1988.
[28], [61].
1989
G. Pantsulaia, On orthogonal families of probability measures, Trans. Georgian
Polytechn. Inst., ser. Mathematical Analysis, v. 350, n. 8, 1989 (in
Russian).
[77].
G. Pantsulaia, Independent families of sets and their applications to measure
theory, Bull. Acad. Sci. GSSR, v. 134, n. 1, 1989 (in Russian).
[71].
G. Pantsulaia, On invariant and quasi-invariant measures on some function
spaces, Bull. Acad. Sci. GSSR, v. 134, n. 3, 1989 (in Russian).
7

[79], [80].
K. Omiadze, On the notion of absolutely negligible sets, Bull. Acad. Sci.
GSSR, v. 135, n. 1, 1989 (in Russian).
[71].
A. Kipiani, On a uniform subset of ω α ×ω α , Bull. Acad. Sci. GSSR, v. 135,
n. 2, 1989 (in Russian).
[28], [61].
A. Kirtadze, On nonseparable extensions of invariant measures, Bull. Acad.
Sci. GSSR, v. 136, n. 2, 1989 (in Russian).
[16], [79].
(*) V. Buldygin, S. Solntsev, Functional Methods in Problems of Summability
of Random Variables, ”Naukova Dumka”, Kiev, 1989, 270 p. (in Russian).
[89].
K. Ciesielski, How good is Lebesgue measure?, Math. Intelligencer, v. 11,
1989.
[71].
P. Zakrzewski, The existence of universal invariant measures on large sets,
Fund. Math., v. 133, n. 2, 1989.
[15].
J.B. Wilker, Tiling R 3 with circles and disks, Geometriae Dedicata, v. 32,
n. 2, 1989.
[88].
A. Kipiani, Uniform sets and isomorphisms of trees, Math. Inst. University
of Wroclaw, Preprint no. 107, 1989.
[28], [61].
Z. Riecanova, On consequences of the Banach-Kuratowski theorem for Stone
algebra valued measures, Mathematica Slovaca, v. 39, issue 1, 1989.
[77].
p.
1990
(*) J.C. Morgan II, Point Set Theory, Marcel Dekker, New York, 1990, 280
[52].
(*) P. Gruber (Ed.), Handbook of Convex Geometry, vol. 1 (680 p.), vol. 2
(700 p.). North-Holland Publ. Co., Amsterdam, 1990.
[3], [4], [9], [34], [35], [38].
8

(*) R. Mabry, Sets which are well-distributed and invariant relative to all
isometry invariant total extensions of Lebesgue measure, Real Analysis Exchange,
vol. 16, 1990-1991.
[71].
P. Zakrzewski, Extensions of isometrically invariant measures on Euclidean
spaces, Proc. Amer. Math. Soc., v. 110, n. 2, 1990.
[15], [81].
1991
(*) V. Boltyanskii, A. Soifer, Geometric Etudes in Combinatorial Mathematics,
(with Introductions by P.Erdös, B.Grünbaum, C.Rousseau), Colorado
Springs, 1991, 248 p.
[3].
V.V. Makeev, On intersections of affine diameters of a convex body, Journal
of Mathematical Sciences, v. 53, n. 5, 1991.
[38].
A. Krawczyk, P. Zakrzewski, Extensions of measures invariant under countable
groups of transformations, Trans. Amer. Math. Soc., v. 326, 1991.
[71].
A. Kirtadze, G. Pantsulaia, On invariant measures in the space R N , Bull.
Acad. Sci. GSSR, v. 141, n. 2, 1991 (in Russian).
[77], [79].
V. Rogava, On resolvable and isodyne topological spaces, Bull. Acad. Sci.
GSSR, v. 141, n. 2, 1991 (in Russian).
[61], [107].
V. Rogava, On sets which do not possess the Baire property, Bull. Acad.
Sci. GSSR, v. 142, n. 2, 1991 (in Russian).
[107], [118].
A. Kirtadze, Nonseparable extensions of invariant measures and the uniqueness
property, Bull. Acad. Sci. GSSR, v. 142, n. 2, 1991 (in Russian).
[16], [71], [79].
G. Pantsulaia, On invariant measures in some function spaces, Trans. Georgian
Techn. Univ., v. 383, n. 10, 1991 (in Russian).
[79].
Z. Zerakidze, A family of measures admitting consistent estimates, New
Trends in Probability and Statistics, vol. 1, 1991, VSP/Mokslas.
[77].
9

M. Balcerzak, Some remarks on sup-measurability, Real Analysis Exchange,
v. 17, 1991-1992.
[56].
1992
(*) S. Kwapień, W. Woyczynski, Random Series and Stochastic Integrals:
Single and Multiple, Birkhauser, Basel, 1992.
[89].
(*) J. Trokhimchuk, Deleted Singularities of Analytic Functions, ”Naukova
Dumka”, Kiev, 1992, 205 p. (in Russian).
[86].
J. Hejduk, Non-Baire sets in category bases, Real Analysis Exchange, v. 18,
n. 2, 1992-1993.
[61], [117].
1993
K. Tschirpke, On the dissection of simplices into orthoschemes, Geometriae
Dedicata, v. 46, n. 3, 1993.
[29].
S. Solecki, On sets nonmeasurable with respect to invariant measures, Proc.
Amer. Math. Soc., v. 119, n.1, 1993.
[15].
S. Solecki, Measurability properties of sets of Vitali type, Proc. Amer. Math.
Soc., v. 119, n. 3, 1993.
[15], [130].
(*) R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge
University Press, Cambridge, 1993.
[89].
(*) G.L. Wise, E.B. Hall, Counterexamples in Probability and Real Analysis,
Oxford University Press, Oxford, 1993.
[57].
(*) J. Pach (ed.), New Trends in Discrete and Computational Geometry,
Springer-Verlag, Berlin, 1993.
[3].
1994
(*) J. Mioduszewski, Topologia przestrzeni euklidesowych, WUS, Warszawa-
Katowice, 1994, 246 p. (in Polish).
10

[86].
G. Rzepecka, W. Wilczynski, On the transformations of measurable sets and
sets with the Baire property, Real Analysis Exchange, v. 20, n. 1, 1994-1995.
[127].
J. Hejduk, On non-Baire sets, Real Analysis Exchange, v. 20, n. 2, 1994-
1995.
[118].
M. Penconek, P. Zakrzewski, The existence of nonmeasurable sets for invariant
measures, Proc. Amer. Math. Soc., v. 121, n. 2, 1994.
[15].
A. Kirtadze, G.Pantsulaia, On uniquely definable extensions of invariant
measures in the space R N , Bull. Acad. Sci. of Georgia, v. 149, n. 2, 1994 (in
Russian).
[71], [79].
G. Pantsulaia, On non-elementary extensions of the Haar measure, Reports
of Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics,
v. 9, n. 2, 1994 (in Russian).
[71].
V.A. Koval, On the rate of convergence of stochastic approximation procedure,
Ukrainian Mathematical Journal, v. 46, n. 8, 1994 (in Russian).
[89].
V.A. Zalgaller, G.A. Los, The solution of Malfatti’s problem, Journal of
Mathematical Sciences, Springer-Verlag, 1994.
[86].
A.M. Kulik, On a set of partial limits of a sequence of weighted sums of
independent random variables, Ukrainian Math. Journal, v. 46, n. 6, 1994.
[89].
(*) R.K. Guy, R.E. Woodrow (editors), The Lighter Side of Mathematics:
Proceedings of the Eugene Strens Memorial, MAA, New York, 1994.
[88].
1995
V.G. Boltyanskii, Solution to the lighting problem for zone bodies, Math.
Notes, v. 58, n. 3-4, 1995 (in Russian).
[4].
J. Hejduk, On the density topology with respect to an extension of Lebesgue
measure, Real Analysis Exchange, v. 21, n. 2, 1995-1996.
[71], [146].
11

P. Zakrzewski, Extending isometrically invariant measures on R n , Real Analysis
Exchange, v. 21, n. 2, 1995-1996.
[24], [71].
G. Pantsulaia, Density points and invariant extensions of Lebesgue measure,
Bull. Acad. Sci. of Georgia, v. 151, n. 2, 1995 (in Russian).
[71].
K. Nikodem, Sz. Wasowicz, A sandwich theorem and Hyers-Ulam stability
of affine functions, Aequationes Mathematicae, v. 49, n. 1, 1995.
[86].
M. Balcerzak, A. Roslanowski, Co-initial families of perfect sets, Journal of
Applied Analysis, v. 1, n. 2, 1995.
[140].
(*) M.A. Lifshits, Gaussian Random Functions, Kluwer Academic Publishers,
Dordrecht, 1995.
[89].
R. Latala, K. Oleszkiewicz, A note of sums of independent uniformly distributed
random variables, Colloq. Math., v. LXVIII, f. 2, 1995.
[89].
1996
M. Balcerzak, D. Rogowska, Making some ideals meager on sets of size of
the continuum, Topology Proceedings, v. 21, 1996, pp. 1-14.
[140].
(*) E. Marczewski, Collected Mathematical Papers, (with comments), Polish
Academy of Sciences, Warszawa, 1996, 724 p.
[31].
J. Hejduk, Non-Baire unions in category bases, Georgian Math. Journal, v.
3, n. 6, 1996.
[122].
J. Hejduk, On abstract density on the real line, Real Analysis Exchange, v.
22, n. 1, 1996-1997.
[71].
P. Zakrzewski, Extending invariant measures on topological groups, Ann.
New York Acad. Sci., v. 788, 1996.
[31].
J. Cobb, Nice decompositions of R n entirely into nice sets are mostly impossible,
Geometriae Dedicata, v. 62, n. 1, 1996.
[88].
12

V.I. Bogachev, Gaussian measures on linear spaces, Journal of Mathematical
Sciences, Springer-Verlag, 1996.
[89].
1997
(*) V. Buldygin, S. Solntsev, Asymptotic Behaviour of Linearly Transformed
Sums of Random Variables, Kluwer Academic Publishers, Dordrecht, 1997, 500
p.
[89].
(*) V. Boltyanskii, H. Martini, P. Soltan, Excursions into Combinatorial
Geometry, Springer-Verlag, Berlin, 1997, 433 p.
[3].
(*) V. Bogachev, Gaussian Measures, ”Nauka”, Moscow, 1997, (in Russian).
[89].
(*) K. Ciesielski, Set-theoretic real analysis, Journ. of Appl. Anal., v. 3, n.
2, 1997, pp. 147-191.
[24], [56], [159].
M. Balcerzak, K. Ciesielski, On the sup-measurable functions problem, Real
Analysis Exchange, v. 23, n. 2, 1997-1998.
[56], [159].
P. Zakrzewski, The uniqueness of Haar measure and set theory, Colloq.
Math., v. 74, n.1, 1997.
[83].
A. Kipiani, One abstract characterization of intervals of cardinal numbers,
Folia Mathem., n. 9, 1997.
[28], [61].
(*) V.G. Boltyanskii, E.D. Baladze, Szokefalvi-Nagy Problem in Combinatorial
Geometry, Nauka, Moscow, 1997.
[3].
1998
(*) P. Howard, J. Rubin, Consequences of the Axiom of Choice, Amer. Math.
Soc., New York, 1998.
[48].
M. Jonsson, J. Wastlund, Partitions of R 3 into curves, Mathematica Scandinavica,
v. 83, n. 2, 1998.
[88].
13

R. Mabry, Some remarks concerning the uniformly gray sets of G.Jacopini,
Rend. Accad. Naz. Sci. Mem. Mat. Appl., (5), 22, 1998.
[46], [71], [148].
L. Bukovsky, Thin sets in a general setting, Tatra Mt. Math. Publ., v. 14,
1998, pp. 241-260.
[140].
V.I. Bogachev, Measures on topological spaces, Journal of Mathematical Sciences,
v. 91, n. 4, 1998, pp. 3033-3156.
[77].
J. Hejduk, Some properties of the density topology with respect to an extension
of the Lebesgue measure, Mathematica Pannonica, 9/2, 1998, pp. 173-180.
[71].
1999
M. Balcerzak, E. Kotlicka, W. Wojdowski, Difference functions for functions
with the Baire property, Aequationes Mathematicae, v. 57, n. 2-3, 1999, pp.
278-287.
[127].
G. Nijaradze, Nonmeasurable sets, Ver. i Mat. Stat., Encyclopedia, Moscow,
1999 (in Russian).
[71].
G. Nijaradze, Differentiation systems, Ver. i Mat. Stat., Encyclopedia,
Moscow, 1999 (in Russian).
[77].
Z. Zerakidze, Disjoint families of measures, Ver. i Mat. Stat., Encyclopedia,
Moscow, 1999 (in Russian).
[49].
(*) H. Martini, V. Soltan, Combinatorial problems on the illumination of
convex bodies, Aequationes Mathematicae, Springer-Verlag, v. 57, 1999.
[3], [4], [47], [63].
Iu.V. Nepomniaschich, A.V. Ponosov, On local operators in some subspaces
of the space L 0 , Matematika, Izv. VUZ, v. 43, n. 6, 1999 (Russian).
[107].
2000
K. Ciesielski, J. Pawlikowski, Small combinatorial cardinal characteristics
and theorems of Egorov and Blumberg, Real Analysis Exchange, v. 26, n. 2,
2000-2001.
14

[194].
M. Balcerzak, A. Wachowicz, Some examples of meager sets in Banach
spaces, Real Analysis Exchange, v. 26, n. 2, 2000-2001, pp. 877-885.
[161].
K. Ciesielski, S. Shelah, Category analogue of sup-measurability problem,
Journ. of Appl. Anal., v. 6, n. 2, 2000.
[56], [159], [194].
(*) D.L. Renfro, Essay on non-differentiability points of monotone functions,
The Math. Forum, Sci. Math., November, 2000.
[194].
D.C. Biles, E. Schechter, Solvability of a finite or infinite system of discontinuous
quasimonotone differential equations, Proc. Amer. Math. Soc., v. 128,
2000.
[159].
M. Balcerzak, K. Ciesielski, D. Rogowska, Remark on meager Σ 0 2-supported
sigma-ideals on the real line, Tatra Mt. Math. Publ. v. 19, 2000.
[140].
A.A. Kuleshov, A representation of a quasi-inverse for a class of linear integral
operators, Differential Equations, 2000 - maik.ru
[77].
2001
Sz. Zeberski, Nonstandard proofs of Eggleston like theorems, Proc. of the
9-th Prague Topological Symposium, Prague, Czech Republic, August 19-25,
2001.
[140].
R. Suabidessen, P. Gartside, B. Heath, Symmetries of the plane and Euclidean
3-space, Department of Mathematics University of Pittsburgh, Summer
report, 2001.
[194].
B.K. Lahiri, I. Lahiri, Vitali sets, Bulletin of the Malaysian Mathematical
Sciences Society, v. 24, n. 2, 2001.
[130].
V.G. Boltyanski, Solution of the illumination problem for bodies with md(M) =
2, Discrete and Computational Geometry, Springer-Verlag, 2001.
[3].
2002
15

(*) M. Väth, Integration Theory: a Second Course, World Scientific Publ.
Co., London-Singapore, 2002, 277 p.
[194].
(*) Handbook of Measure Theory, volumes 1 - 2, North-Holland Publishing
Co., Elsevier, Amsterdam, 2002.
[15], [46], [53], [71], [120], [130], [152], [162].
(*) R.J. Gardner, The Brunn-Minkowski inequality, Bull. Amer. Math.
Soc., v. 39, n. 3, 2002.
[195].
J. Cichoń, A. Jasiński, A note on algebraic sums of subsets of the real line,
Real Analysis Exchange, v. 28, n. 2, 2002 - 2003.
[147], [152].
J. Hejduk, On density topologies with respect to invariant σ-ideals, Journal
of Applied Analysis, v. 8, n. 2, 2002.
[146].
G. Pantsulaia, Duality of measure and category in infinite-dimensional separable
Hilbert space l 2 , International Journal of Mathematics and Mathematical
Sciences, Hindawi Publ. Corp., 2002.
[73], [77], [101].
G. Alsmeyer, The minimal subgroup of a random walk, Journal of Theoretical
Probability, v. 15, n. 2, 2002.
[166].
(*) D.A. Vladimirov, Boolean Algebras in Analysis, Springer-Verlag, Berlin,
2002, 632 p.
[71].
R. Filipow, Wlasnosc roznicy w sensie de Bruijna dla rodzin funkcji mierzalnych,
Thesis, Institute of Mathematics of Polish Academy of Sciences, 2002 (in
Polish).
[147], [148].
p.
2003
(*) M. Trott, The Mathematica Guide Book, Birkhäuser, Basel, 2003, 1000
[194].
J. Cichoń, J. Kraszewski, The properties of measure and category in generalized
Cantor spaces, Preprint of Institute of Mathematics, Wroclaw University,
2003.
[207].
16

J. Kraszewski, Transitive properties of ideals, Preprint of Institute of Mathematics,
Wroclaw University, 2003, 20 p.
J. Kraszewski - math.uni.wroc.pl
[140].
G. Pantsulaia, On separation properties for families of probability measures,
Georgian Mathematical Journal, v. 10, n. 3, 2003.
[71], [77], [108], [123].
M. Balcerzak, E. Kotlicka, Steinhaus property for products of ideals, Publicationes
Mathematicae Debrecen, 2003.
[161], [194].
S. Solecki, Extensions of translation invariant sigma-ideals, Israel Journal of
Mathematics, v. 135, 2003.
[15], [130], [162].
J. Angel Cid, Rodrigo Lopez Pouso, On first order ordinary differential equations
with nonnegative right-hand sides, Non-linear Analysis: Theory, Methods
and Applications, v. 52, n. 8, 2003.
[194].
J. Angel Cid, On uniqueness criteria for systems of ordinary differential
equations, Journal of Math. Analysis and Applications, v. 281, issue 1, 2003.
[194].
(*) V.I. Bogachev, Foundations of measure theory, vol. 1-2, Dynamics,
Moscow, 2003 (in Russian). English version of this book was published by
Springer-Verlag.
[46], [71], [77], [120], [123], [162], [194].
J. Ewert, S.P. Ponomarev, On the convergence of ω-primitives, Math. Slovaca,
v. 53, n. 1, 2003, pp. 59-66.
[152].
R. Filipow, On the difference property of the family of functions with the
Baire property, Acta Mathematica Hungarica, v. 100, n. 1-2, 2003, pp. 97-104.
[140].
2004
(*) Ch. Castaing, P.R. de Fitte, M. Valadier, Young Measures on Topological
Spaces: With Applications to Control Theory, Springer-Verlag, Heidelberg,
2004, 320 p.
[73].
(*) K. Ciesielski, J. Pawlikowski, The Covering Property Axiom, CPA, Cambridge
University Press, Cambridge, 2004, 174 p.
17

[194].
E. Zoli, On the equivalence between CH and the existence of certain I-Luzin
subsets of R, Georgian Mathematical Journal, v. 11, n. 1, 2004.
[161].
G. Pantsulaia, An application of independent families of sets to the measure
extension problem, Georgian Mathematical Journal, v. 11, n. 2, 2004.
[31], [61], [71], [77], [113], [134], [157], [162].
G. Pantsulaia, Relations between shy sets and sets of ν-measure zero in Solovay’s
model, Bull. of Polish Acad. of Sci., v. 52, n. 1, 2004.
[79], [140].
G. Pantsulaia, On an invariant Borel measure in Hilbert space, Bull. of
Polish Acad. of Sci., v. 52, n. 1, 2004.
[79].
L. Alexidze, Z. Zerakidze, Optimal consistent estimates connected with a
stochastic system, Bull. of the Georgian Acad. of Sciences, v. 169, n. 1, 2004.
[77].
L. Alexidze, Z. Zerakidze, On some properties of strongly and weakly separable
statistical structures connected with a stochastic system, Bull. of the
Georgian Acad. of Sciences, vol. 1, n. 2, 2004.
[77].
L. Alexidze, Z. Zerakidze, Construction of Gaussian homogeneous isotropic
statistical structures connected with a stochastic system, Bull. of Georgian Acad.
of Sciences, v. 169, n. 3, 2004.
[77].
M. Kysiak, Nonmeasurable algebraic sums of sets of reals, The Bulletin of
Symbolic Logic, v. 11, n. 2, 2004-2005.
[147].
(*) G. Plebanek, Measures on Topological Spaces, (in Polish), Lecture Course
2004-2005, Wroclaw University,
www.math.uni.wroc.pl/ grzes/dydaktyka/wstep.pdf
[140].
(*) M. Kysiak, Zbiory niemierzalne i algebraiczna struktura prostej rzeczywistej,
Konwersatorium dla doktorantow, UW, 2004.
[147].
K. Chmielewska, Strong sup-measurability of functions of two variables, Tatra
Mt. Math. Publ., v. 28, 2004.
[56], [159].
18

Ya. I. Zyelyk, M.M. Lychak, Computer technology of interval-set analysis in
MATLAB, Cybernetics and Systems Analysis, v. 40, issue 1, 2004.
[194].
Ya. I. Zyelyk, M.M. Lychak, Software-Hardware Systems, Cybernetics and
Systems Analysis, 2004 - ingentaconnect.com
[194].
M. Filipczak, J. Hejduk, On topologies associated with the Lebesgue measure,
Tatra Mt. Math. Publ., v. 28, 2004.
[194].
(*) Qi Guo, Minkowski measure of asymmetry and Minkowski distance for
convex bodies, Uppsala Dissertations in Mathematics, v. 35, Uppsala, 2004.
[38].
(*) H. Pursiainen, The algebraic interpretation of consistency in aggregation
and quasilinear index numbers, University of Helsinki, 2004.
[194].
(*) J. Borsik, J. Haluska, Real Functions, vol. 1, Tatra Mountains Math.
Publ., Slovak Academy of Sciences, Bratislava, 2004.
[56], [159].
(*) J. Borsik, J. Haluska, Real Functions, vol. 2, Tatra Mountains Math.
Publ., Slovak Academy of Sciences, Bratislava, 2004.
[194].
(*) I. Grattan-Guinness, Bhuri Singh Yadav, History of the Mathematical
Sciences, New Delhi, 2004.
[220].
(*) V.I. Subbotin, Strongly symmetric polyhedra, Thesis, Novocherkassk,
2004 (Russian).
[25].
2005
A. Kirtadze, G. Pantsulaia, On null-sets in infinite-dimensional Banach
spaces, Proc. A. Razmadze Math. Institute, v. 139, 2005.
[140].
P. Blaszczyk, On the mode of existence of the real numbers, Analecta Husserliana,
Springer-Verlag, v. 88, 2005.
[140].
V. Soltan, Pairs of convex bodies with centrally symmetric intersections of
translates, Discrete Comp. Geometry, v. 33, 2005.
[4].
19

J. Jachymski, A non-linear Banach-Steinhaus theorem and some meager sets
in Banach spaces, Studia Math., v. 170, n. 3, 2005.
[194].
A. Kirtadze, On the method of direct products in the theory of quasi-invariant
measures, Georgian Mathematical Journal, v. 12, n. 1, 2005.
[53], [71], [162], [201].
A. Kirtadze, On the uniqueness property for invariant measures, Georgian
Mathematical Journal, v. 12, n. 3, 2005.
[16], [71], [79], [83], [158], [162].
A. Kirtadze, On the uniqueness property for invariant measures in infinitedimensional
product-spaces, International Conference: Modern Problems and
New Trends in Probability Theory, Chernivtsi, Ukraine, June 19-26, 2005.
[162].
M. Kysiak, E. Zoli, Set-theoretic properties of Schmidt’s ideal, Georgian
Mathematical Journal, v. 12, 2005.
[140], [161].
H. Okamoto, A remark on continuous nowhere differentiable functions, Proceedings
of the Japan Academy, Ser. A, Mathem. Sciences, v. 81, n. 3, 2005.
[194].
G. Mora, The Peano curves as limits of alpha-dense curves, Review R. Acad.
Cien. Ser. A. Math. (RACSAM), v. 99, n. 1, 2005.
[194].
D.L. Renfro, Intersections of measurable sets, May, 2005,
sci.tech-archive.net (sci.math.). Math. Forum,
mathforum.org/kb/plaintext.jspa?messageID=3767449
[194].
V.G. Boltyanskii, A counterexample to an illumination conjecture, Doklady
Mathematics, v. 72, n. 1, 2005.
[3].
F.G. Dorais, R. Filipow, Algebraic sums of sets in Marczewski-Burstin algebras,
Real Analysis Exchange, v. 31, n. 1, 2005-2006.
[147].
A. Kirtadze, On some questions of the theory of dynamical and quasidynamical
systems, Proc. of the IV-th Symposium of the Georgian Mathematical
Union, 14-16 November, 2005 (in Georgian).
[79].
(*) A. Liu, B. Shawyer (editors), A Taste of Mathematics, v. 9, Canadian
Math. Society, Ontario, 2005.
20

[89].
D.L. Renfro, Outer measure of the Vitali non-measurable set, Math. Forum
Discussions,
The Math Forum@Drexel, January, 2005, mathforum.org/kb/thread.jspa
[216].
(*) A. Malikov, Projection and study of properties of relational databases
normalized via sampling and joining operations, Thesis, Stavropol, 2005 (in
Russian).
[107].
(*) V. Soltan, Affine diameters of convex bodies - a survey, Expositiones
Mathematicae, v. 23, issue 1, 2005, pp. 47-63.
[35], [38].
2006
G. Barbieri, D. Dikranjan, C. Milan, H. Weber, t-dense subgroups of topological
Abelian groups, Questions and Answers in General Topology, v. 24, 2006.
[140].
A. Roslanowski, S. Shelah, Measured creatures, Israel Journal of Mathematics,
v. 151, 2006.
[194].
Miara Dieudonne, Wikipedia (wolna encyklopedia), 2006.
www.pl.wikipedia.org/wiki
[150].
(*) D.L. Renfro, Exotic Functions, 2006.
sci.tech-archive.net/pdf/Archive/sci.math/2006-10
[194].
Sz. Zeberski, R. Ralowski, Complete nonmeasurability in regular families of
small sets, International Conference on Set-Theoretic Topology, Kielce, Poland,
August 20-25, 2006.
[152].
(*) A. Kirtadze, Some Aspects of the Theory of Dynamical and Quasi-
Dynamical Systems, Georgian Technical University Press, Tbilisi, 2006, 270
p. (in Georgian).
[24], [53], [61], [68], [71], [77], [79], [120], [159], [162], [194].
(*) J.I.U. Garcia, Aspectos Geometricos y Topologicos de las Curvas α-
Densas, Thesis Doctoral, Universidad de Alicante, 2006.
[194].
(*) C. Schütt, Masstheorie, lecture course, 2006, 219 pages.
21

analysis.math.uni-kiel.de/schuett/masstheo.pdf
[194].
D.L. Renfro, Luzin’s theorem, 2006.
sci.tech-archive.net/Archive/sci.../msg04555.html
[216], [228].
B.K. Lahiri, I. Lahiri, Vitali and metrically perfect sets, Analele Stiintifice
Ale Universitatii ”AL.I. CUZA” Iasi, v. LII, s. I, Matematica, 2006, f. 1.
[130].
2007
Sz. Zeberski, On completely nonmeasurable unions, Mathematical Logic
Quarterly, v. 53, issue 1, 2007.
[207], [228].
J. Cichon, M. Morayne, R. Ralowski, Cz. Ryll-Nardzewski, Sz. Zeberski,
On nonmeasurable unions, Topology and its Applications, v. 154, issue 4, 2007.
[207].
A. Kirtadze, G. Pantsulaia, Lebesgue nonmeasurable sets and the uniqueness
of invariant measures in infinite-dimensional vector spaces, Proc. A.Razmadze
Mathem. Institute, v. 143, 2007.
[79], [101], [140].
A. Kirtadze, A method of homomorphisms in the theory of invariant and
quasi-invariant measures, Intern. Conference: Skorokhod Space. 50 years on.,
Abstracts, Part 1, Kyiv, 2007.
[71], [79], [219], [227].
G. Pantsulaia, On an inductive limit of invariant measures, Intern. Conference:
Skorokhod Space. 50 years on., Abstracts, Part 1, Kyiv, 2007.
[73], [79].
(*) Valeriu Anisiu, Modern aspects of topology and measure theory, Titular
Curs, Universitatea Babes-Bolyai Din Cluj-Napoca Matematica Si Informatica,
2007 (in Rumanian).
[194].
(*) Wilman Brito, El Teorema de Categoria de Baire y Aplicaciones, 2007.
[194].
J. Hejduk, A. Loranty, On lower and semi-lower density operators, Georgian
Mathematical Journal, v. 14, n. 4, 2007.
[146].
A.P. Kirtadze, On non-separable invariant measures, Edward Marczewski
Centennial Conference, Measure Theory, Bedlewo, 9-15 September, 2007.
22

www.math.uni.wroc.pl/ measure07
[71], [162], [227].
A.P. Kirtadze, Some applications of surjective homomorphisms in the theory
of invariant and quasi-invariant measures, Proc. A. Razmadze Math. Institute,
v. 144, 2007.
[71], [79], [162], [219], [227].
A.P. Kirtadze, On some estimates of topological weights of left-invariant
measures on uncountable solvable groups, Proc. A. Razmadze Mathematical
Institute, v. 145, 2007.
[71], [162], [195], [227].
M. Balcerzak, On completeness generated by convergence with respect to a
σ-ideal, Real Analysis Exchange, v. 32, n. 2, 2007.
[140].
(*) G. Pantsulaia, Invariant and Quasiinvariant Measures in
Infinite-Dimensional Topological Vector Spaces, Nova Science Publishers,
Inc., New York, 2007.
[61], [71], [77], [79], [80], [113], [123], [134], [140], [146], [152],
[162].
Sz. Zeberski, On weakly measurable functions, Math. Inst. Wroclaw University,
2007 (preprint),
www.math.uni.wroc.pl/ szebe/papers/bp7482.ps
[207].
J. Cichon, J. Kraszewski, On some new ideals on the Cantor and Baire
spaces, Math. Inst. Wroclaw University, preprint, 2007.
www.math.uni.wroc.pl/ kraszew
[207].
R. Filipow, On the difference property of families of measurable functions,
2007,
math.univ.gda.pl/ rfilipow/papers/files.
[140], [152].
(*) B. Weglorz, Introduction to Set Theory, Lecture Course, 2007, Institute
of Mathematics and Computer Science, Polytechn. Wroclaw. -
w3.im.pwr.wroc.pl/opisy/eprint.php?code=MAP2110
[140].
(*) M. Kysiak, Deskryptywna Teoria Mnogosci, course of lectures, 2007 (in
Polish).
www.mimuw.edu.pl/ mkysiak/dtm.html
[140].
23

Works on functional equations and inequalities in several variables - XXI,
Aequationes Mathematicae, Springer-Verlag, 2007.
[228].
H. Okamoto, M. Wunsch, A geometric construction of continuous, strictly
increasing singular functions, Proceedings of Japan Academy, Ser. A, Mathematical
Sciences, v. 83, n. 7, 2007.
[194].
(*) J. Elstrodt, Measure and Integration Theory, Springer-Verlag, Heidelberg,
2007 (in German).
[194], [228].
He Zhi-Cheng, Shen Shi-Ying, Zhang Yue-Hui, Constructions of generalized
Vitali’s nonmeasurable sets, Journal of Southwest University, Natural Science
ser., v. 29, n. 10, 2007 (in Chinese).
[130], [216].
XXVI Ogolnopolski Sejmik Matematykow, 2007 (in Polish),
www.spinor.stolorz.pl/konkursy/sejmik/XXVI/tematy.pdf
[194].
V. Boltyanski, H. Martini, Illumination of direct vector sums of convex bodies,
Studia Scientiarum Mathematicarum Hungarica, v. 44, n. 3, 2007.
[3].
A. Madrecki, The Riemann hypothesis - an elementary analytic approach
based on complex Laplace transform, Arxiv preprint, arXiv: 0706.1968, 2007.
[15].
(*) P. Blaszczyk, Analiza Filozoficzna Rozprawy R. Dedekinda ”Stetigkeit
und Irrationale Zahlen”, Prace Monograficzne, WNAP, Krakow, 2007 (in Polish).
[140].
El Problema de la Medida, 21 pages, 2007.
grupofundamental.files.wordpress.com/2007/03/problemasmedida.pdf
[163].
D.L. Renfro, How do mathematicians call a ”swiss cheese” set over the real
line?, 2007.
Archive/sci.math, 02-2007, sci.tech-archive.net
[194].
2008
B.K. Lahiri, I. Lahiri, Category Vitali sets, Analele Stiintifice Ale Universitatii
”AL.I. CUZA” Din Iasi, (S.N.) Matematica, v. LIV, f. 2, 2008, pp.
445-454.
24

[130].
M. Rodriguez Chala, Infinito más uno: infinito, Granada, 2008, 12 p.
www.nablanoesunvector.org/archivos/trabajos/infinito.pdf
[228].
M. Gazor, A measure-theoretical version of the Alexandrov theorem, Georgian
Mathematical Journal, v. 15, n. 1, 2008.
[77], [216].
A. Kipiani, On automorphism groups of ω-trees, Georgian Mathematical
Journal, v. 15, n. 1, 2008.
[71].
S. Balasuriya, Teaching time savers: reacting to analysis, MAA Focus, v.
28, issue 4, 2008.
[228].
G.R. Pantsulaia, On generators of shy sets on Polish topological vector spaces,
New York Journ. Math., v. 14, 2008.
[79], [140].
G.R. Pantsulaia, On intersection of problems of theoretical statistics and set
theory, Far East Journal of Theoretical Statistics, v. 25, n. 2, 2008.
[77], [140].
H. Weber, E. Zoli, Finite partitions of topological groups into congruent thick
subsets, Journal of Applied Analysis, v. 14, n. 1, 2008.
[140], [152].
(*) O. Deiser, Reelle Zahlen, Springer-Verlag, Berlin, 2008 (in German).
[31].
R. Ralowski, P. Szczepaniak, Sz. Zeberski, A generalization of Steinhaus
theorem and some nonmeasurable sets, preprint, 2008.
www.im.pwr.pl/ ralowski/nauka/Cantor
[147].
I. Loeb, Factoring Out Intuitionistic Theorems: Continuity Principles and
the Uniform Continuity Theorem, Lecture Notes in Computer Science, Springer-
Verlag, v. 5028, 2008.
[228].
E. Shmileva, Shifted small deviations and Chung LIL for symmetric stable
processes, arXiv : 0811.2583v1 [math PR] 17 Nov 2008.
[91].
M. Ziegler, Real computation with least discrete advice: a complexity theory
of nonuniform computability, arXiv: 0811.3782, November 2008.
25

[194].
Z. Zerakidze, On some properties of statistical structures, Reports of Enlarged
Session of the Seminar of I. Vekua Institute of Applied Mathematics, v.
22, 2008.
[228].
L. Alexidze, Z. Zerakidze, About strongly and weakly separable statistical
structures, Reports of Enlarged Session of the Seminar of I. Vekua Institute of
Applied Mathematics, v. 22, 2008.
[216].
G. Pantsulaia, On a certain example of a non-locally compact non-abelian
Polish group which does not satisfy ccc, Sokhumi State University Proceedings,
v. IV, Mathematics and Computer Science Series, Tbilisi, 2008, pp. 94-99.
[140].
2009
P. Zakrzewski, On nonmeasurable selectors of countable group actions, Fund.
Math., v. 202, 2009, pp. 281-294.
[234].
A. Kirtadze, Some remarks on the metrical transitivity of invariant and
quasi-invariant measures, Acta Universitatis Carolinae, Phys.-Math. Ser., v.
49, 2009.
[71], [79], [162], [240].
A. Kirtadze, On the uniqueness property of σ-finite invariant measures, International
Conference: Stochastic Analysis and Random Dynamics, Abstracts,
June 14-20, 2009, Lviv, Ukraine.
[162].
G. Pantsulaia, On a certain problem of E. Szpilrajn for non-separable complete
metric spaces, International Conference: Stochastic Analysis and Random
Dynamics, Abstracts, June 14-20, 2009, Lviv, Ukraine.
[77].
G. Pantsulaia, On Liouville-type theorems for generators of shy sets in the
infinite-dimensional Polish topological vector space R N , International Conference:
Stochastic Analysis and Random Dynamics, Abstracts, June 14-20, 2009,
Lviv, Ukraine.
[79].
Z. Zerakidze, G. Sokhadze, On some properties of strongly and weakly separable
statistical structures in Banach space of measures, International Conference:
Stochastic Analysis and Random Dynamics, Abstracts, June 14-20, 2009, Lviv,
Ukraine.
26

[77].
K. Neu, A few results on Archimedean sets, Real Analysis Exchange, v. 34,
n. 1, 2009.
[136], [161].
(*) M. Wunsch, Asymptotics of nonlinear diffusion and fluid dynamics equations,
Dr. Thesis, Universität Wien, 2009, 120 p.
[194].
T. Tetunashvili, To the problem of teaching mathematics: once again on
logical and set-theoretical approach, Science and Technologies, n. 7-9, 2009,
Tbilisi (in Georgian).
[239], [245], [248], [249].
(*) M. Kolar, Kmitajici znamenkove miry, Univerzity Karlovy, Praha, 2009.
[194].
(*) S. Semmes, An introduction to some aspects of functional analysis, 2:
Bounded linear operators, Rice University, 2009.
[162].
(*) A. Göpfert, T. Riedrich, Ch. Tammer, Angewandte Funktionalanalysis,
Vieweg+Teubner Verlag, Berlin, 2009.
[161].
M. Balcerzak, Sz. Gläb, On the Laczkovich-Komjáth property of sigmaideals,
Topology and its Applications, 2009.
[140].
A. Kirtadze, On functions with thick graphs and extensions of measures,
Proc. A. Razmadze Math. Inst., v. 150, 2009.
[220], [228], [236].
Egorov’s Theorem, Wikipedia, 2009.
[194].
R.M. Aron, F.J. Garcia-Pacheco, D. Perez-Garcia, J.B. Seoane-Sepulveda,
On dense lineability of sets of functions on R, Topology, 2009.
[228].
G. Pantsulaia, On ordinary and standard Lebesgue measures on R ∞ , Bulletin
of the Polish Academy of Sciences, Mathematics, v. 57, no. 3-4, 2009.
[140].
T. Kania, O zbiorze Sierpińskiego, Katowice, 2009.
T Kania - knm.katowice.pl
[216].
27

K. Neu, Almost isometry-invariant sets and shadings, Real Analysis Exchange,
v. 35, n. 2, 2009, pp. 391-402.
[161].
A. Kirtadze, On applications of methods of infinite combinatorics in the
theory of invariant and quasi-invariant measures, Fifth Congress of Mathematicians
of Georgia, Abstracts of Contributed Talks, Batumi-Kutaisi, October 9-12,
2009, p. 21 (in Georgian).
[61].
T. Kania, Aksjomat Martina, Katowice, 2009.
T Kania - knm.katowice.pl
[140].
(*) N.I. Shliahova, Exploiting optimal mathematical models of distributed
information systems, Thesis, Stavropol, 2009 (Russian).
[107].
J. Brandts, S. Korotov, M. Krizek, J. Solc, On non-obtuse simplicial partitions,
SIAM Review, v. 51, n. 2, 2009, pp. 317-335.
[29].
(*) A. Liu, B. Shawyer (editors), Problems from Murray Klamkin: The
Canadian Collection, Mathematical Association of America, 2009.
[89].
2010
Wapedia-Wiki: Mesure de Lebesgue, 2010.
[195].
J.L. Gamez, G.A. Munoz-Fernandez, J.B. Seoane-Sepulveda, Lineability and
additivity in R R , Journal of Mathematical Analysis and Applications, v. 369,
issue 1, 2010, pp. 265-272.
[220].
J.L. Gamez-Merino, G.A. Munoz-Fernandez, V.M. Sanchez, J.B. Seoane-
Sepulveda, Sierpiński-Zygmund functions and other problems of lineability, Proc.
Amer. Math. Soc., 2010.
[228].
K. Diab, Mazurkiewicz’s theorem and the well-ordering principle, Exchange
Interactions, 2010.
kenandiab.wordpress.com/author/kenandiab/
[261].
A. Gavrilut, A. Croitoru, N. Mastorakis, Fuzzy diffused set multifunctions,
Proceedings of the 4th WSEAS International Conference on Computational
Intelligence, April 20-22, 2010, pp. 148-153 (Romania).
28

[220], [228].
(*) Chuan Zhang, Integration and Measure Theory, Lecture Course, 2010.
sites.google.com/site/chuanzhang04/.../2010-spring
[163].
R. Mabry, Stretched shadings and a Banach measure that is not scale-invariant,
Fund. Math., v. 209, 2010, pp. 95-113.
[71], [161].
N.H. Bingham, A.J. Ostaszewski, Beyond Lebesgue and Baire II: Bitopology
and measure-category duality, Colloq. Math., v. 121, 2010, pp. 225-238.
[127].
A.J. Ostaszewski, Beyond Lebesgue and Baire III: Analyticity and shiftcompactness,
Department of Mathematics, London School of Economics and
Political Science, preprint, 2010, 40 p.
www.math.lse.ac.uk
[127].
A. Gavrilut, A. Croitoru, N. Mastorakis, Diffusion and semi-convexity of
fuzzy set multifunctions, WSEAS Transactions on Mathematics, v. 9, issue 7,
2010.
[220], [228].
G. Pantsulaia, On T-shy sets in Radon metric groups, Journal of Mathematical
Sciences: Advances and Applications, v. 5, n. 1, 2010, pp. 149-185.
[77], [79], [140].
Zbiór Bernsteina, Wikipedia - Wolna encyklopedia, 2010.
[216].
J. Kuznetsova, Nonmeasurable unions of sets and continuity of group representations,
arXiv: 1010.0999, October 2010.
[216], [218], [223].
R. Ralowski, S. Zeberski, On nonmeasurable images, Czechoslovak Mathematical
Journal, v. 60, n. 2, 2010, pp. 423-434.
[147].
(*) N.H. Bingham, A.J. Ostaszewski, Normed versus topological groups: Dichotomy
and duality, Dissertationes Math., 2010.
www.math.lse.ac.uk
[127].
T. Tetunashvili, On some aspects of group theory in higher mathematics
courses, Georgian International Journal of Science and Technology, v. 3, n. 1,
2010.
[71], [216], [239], [249], [266].
29

Hu Guannan, Two Bernstein sets and Luzin sets, Journal of Chengdu University,
Natural Science Edition, v. 29, n. 2, 2010.
[216].
B. Bogosel, Darboux Functions, Universitatea de Vest Timisoara, Romania,
2010, pp. 1-8.
mathproblems123.files.wordpress.com/2010/07/strange-functions.pdf
[228].
Z. Zerakidze, G. Saatashvili, Construction of stationary statistical structures,
The Third International Conference: ”Problems of Cybernetics and Informatics”,
September 6-8, 2010, Baku, Azerbaijan.
[77].
L. Alexidze, Z. Zerakidze, On some properties of strongly and weakly separable
Gaussian homogeneous isotropic statistical structures in Banach space of
measures, The Third International Conference: ”Problems of Cybernetics and
Informatics”, September 6-8, 2010, Baku, Azerbaijan.
[77].
J. Cichon, P. Szczepaniak, Hamel-isomorphic images of the unit ball, Mathematical
Logic Quarterly, v. 56, issue 6, 2010, pp. 625-630.
[130].
(*) J.F. Sanchez, Contribuciones al estudio de Funciones Peculiares y Teoria
de Copulas, Universidad de Almeria, Almeria, 2010, 191 p.
[194].
G. Matusik, On the lattice generated by Hamel functions, Real Analysis
Exchange, v. 36, n. 1, 2010, pp. 65-78.
[236].
(*) J.J. Rotman, Advanced Modern Algebra, American Mathematical Society,
New York, 2010.
[216].
2011
M. Stas, Perfect set property, 39th Winter School in Abstract Analysis, Section
of Set Theory, Hejnice, Czech Republic, 29th January - 5th February, 2011.
[228].
A. Kipiani, On representation of abstract groups as automorphism groups of
graphs, 39th Winter School in Abstract Analysis, Section of Set Theory, Hejnice,
Czech Republic, 29th January - 5th February, 2011.
[61].
30

G.R. Pantsulaia, On ordinary and standard products of infinite family of σ-
finite measures and some of their applications, Acta Mathematica Sinica, v. 27,
n. 3, 2011.
[61], [71], [113].
V.A. Chatyrko, On countable unions of nonmeager sets in hereditarily Lindelöf
spaces, P-adic Numbers, Ultrametric Analysis, and Applications, v. 3, n.
1, 2011, pp. 1-6.
[216].
Fucai Lin, Shou Lin, Pseudobounded or ω-pseudobounded paratopological
groups, Filomat, v. 25, n. 3, 2011, pp. 91-101.
[216].
P. Zakrzewski, On Borel sets belonging to every invariant ccc σ-ideal on 2 N ,
preprint, 2011, 11 p. mimuw.edu.pl
[130].
(*) A. Prosperetti, Advanced Mathematics for Applications, Cambridge University
Press, Cambridge, 2011.
[228].
(*) G. Pantsulaia, On Generators of Shy Sets in Polish Groups, Nova Science
Publ., Inc., New York, 2011.
[61], [71], [73], [77], [79], [80], [92], [113], [123], [134], [152],
[162], [222], [235].
G. Pantsulaia, On uniformly distributed sequences of an increasing family of
finite sets in infinite-dimensional rectangles, Real Analysis Exchange, v. 36, n.
2, 2010-2011.
[77].
V. Chatyrko, V. Nyagaharwa, On the families of sets without the Baire
property generated by the Vitali sets, P -adic Numbers, Ultrametric Analysis,
and Applications, v. 3, n. 2, 2011, pp. 100-107.
[216].
P. Niemiec, A note on invariant measures, Opuscula Mathematica, v. 31, n.
3, 2011, pp. 425-431.
[162].
(*) L. Bukovský, The Structure of the Real Line, Birkhäuser, Basel, 2011,
536 p.
[140].
A. Kirtadze, On measurability of functions and extensions of measures,
Abstracts of the 2nd International Conference of the Georgian Mathematical
Union, September 15-20, Batumi, 2011, pp. 41-42.
31

[220], [236].
M. Beriashvili, Mathematics before and after Gödel, Abstracts of the 2nd
International Conference of the Georgian Mathematical Union, September 15-
20, Batumi, 2011, pp 154-155.
[266].
T. Kasrashvili, Algebraic curves and their properties in Higher Mathematics
course, Abstracts of the 2nd International Conference of the Georgian Mathematical
Union, September 15-20, Batumi, 2011, p. 156.
[239].
T. Tetunashvili, On equidecomposability paradoxes, Abstracts of the 2nd International
Conference of the Georgian Mathematical Union, September 15-20,
Batumi, 2011, p. 159.
[71].
T. Kasrashvili, A. Kirtadze, On some combinatorial properties of Diophantine
sets in Euclidean spaces, Abstracts of the 10th International Conference on
Geometry and Applications, September 03-09, Varna, 2011, pp. 34-35.
[86].
S. Gläb, LK property for sigma-ideals, Topology and its Applications, v.
158, issue 1, 2011, pp. 93-100.
[140].
A. Bartoszewicz, S. Gläb, D. Pellegrino, J.B. Seoane-Sepulveda, Algebrability,
non-linear properties, and special functions,
arXiv:1109.3674v1 [math.FA] 16 Sep 2011
[228].
Choquet Theory, 2011, zml.name/?z=Choquet-theory
[259].
Difference between a partial selector and a selector, MathOverflow, 2011,
mathoverflow.net/questions/
[216].
Resolvable space, Wikipedia, 6 November, 2011.
[228].
Hamel basis and additive functions, November 7, 2011,
thales.doa.fmph.uniba.sk/sleziak/texty/rozne/pozn/tm/hamel.pdf
[194].
G. Drago, P.D. Lamberti, P. Toni, A ”bouquet” of discontinuous functions
for beginners in mathematical analysis, Amer. Math. Monthly, v. 118, n. 9,
2011.
[228].
32

R. Mabry, Recent ”improvements” of the Lebesgue measure, Real Analysis
Exchange, Summer Symposium, 2011, pp. 53-54.
[165].
(*) J. Mioduszewski, Wyklady z Topologii, Wydawnictwo Uniwersytetu Slaskiego,
Katowice, 2011.
[140].
Pathologies and Paradoxes in Mathematics, XXX SMS’ Session, Szczyrk,
29th April - 3rd May, 2011.
[228].
I.P. Blazhievska, Correlogram estimation of response functions of linear systems
in scheme of some independent samples, Theory of Stochastic Processes,
v. 17 (33), n. 1, 2011, pp. 16-27.
[89].
2012
A. Basse-O’Connor, J. Rosinski, Characterization of the finite variation
property for a class of stationary increment infinitely divisible processes,
arXiv:1201.4366v1 [math.PR] 20 Jan 2012.
[194].
H.I. Miller, A.J. Ostaszewski, Group action and shift-compactness, Journal
of Mathematical Analysis and Applications, v. 392, issue 1, 2012, pp. 23-39.
[127].
T. Kasrashvili, Discrete point systems in Euclidean spaces and invariants of
associated continuous images, Science and Technologies, n. 1-3, 2012, pp. 7-16
(in Georgian).
[47], [239], [266].
Theoreme de Steinhaus - Wikipedia, 2012
fr.wikipedia.org/wiki/Theoreme-de-Steinhaus
[161].
S. Maschio, Teoria della misura e teoria degli insiemi, 2012, 10 p.
selp/apnetwork.it/userfiles/alessio/file/.../siena-maschio.pdf
[216].
S. Dhami, Ali al-Nowaihi, Philanthropy, multiple equilibria and optimal public
policy, 08 April, 2012, 40 p.
www.le.ac.uk/economics/sd106/Philanthropy.pdf
[228].
M. Ziegler, Real computation with least discrete advice: A complexity theory
of nonuniform computability with applications to effective linear algebra, Annals
of Pure and Applied Logic, v. 163, issue 8, 2012, pp. 1108-1139.
33

[228].
P.B. Ramkumar, Higher dimensional image analysis using Brunn-Minkowski
theorem, convexity and mathematical morphology, Journal of Information Engineering
and Applications, v. 2, n. 4, 2012, pp. 1-8.
[195].
E. Dupree, B. Mathes, Functions with dense graphs, 2012, pp. 1-3.
E Dupree... - 2012 - colby.edu
[228].
T.L. Gill, G.R. Pantsulaia, W.W. Zachary, Constructive analysis in infinitely
many variables, Communications in Mathematical Analysis, v. 13, n. 1, 2012,
pp. 107-141.
[79].
B. Bogosel, Functions with the intermediate value property, Gazeta Matematica,
Seria A, ANUL XXX (CIX), n. 1-2, 2012, pp. 1-8.
[228].
J.L. Gamez-Merino, J.B. Seoane-Sepulveda, An undecidable case of lineability
in R R , 1-5 pp.
arXiv: 1207.2906v1 [math. FA] 12 Jul 2012
[228].
(*) G. Saatashvili, On stationary statistical structures, Thesis, Georgian
Technical University, 2012, pp. 1-111 (in Georgian).
[61], [71], [77], [80], [140].
A. Kirtadze, Non-separable extensions of invariant measures and the uniqueness
property, International Conference dedicated to 120-th anniversary of Stefan
Banach, Abstracts, September 17-21, Lviv, Ukraine, 2012.
[16].
J. Hejduk, A. Loranty, Remarks on the topologies in the Lebesgue measurable
sets, Demonstratio Mathematica, v. XLV, no. 3, 2012, pp. 657-665.
[146].
(*) M. Rupp, Theorems and Problems in Functional Analysis - The Answer
Book 1: Elements of Set Theory and Topology, Springer, 2012.
[228].
R. Filipow, Cardinal characteristics of quotient Boolean algebras P (ω)/I and
ideal convergence of sequences of functions, 12 p.
RL FILIPOW - 2012 - rfilipow.mat.ug.edu.pl
[194].
2013
34

F. Dorais, R. Filipow, T. Natkaniec, On some properties of Hamel bases
and their applications to Marczewski measurable functions, Central European
Journal of Mathematics, v. 11, issue 3, 2013, pp. 487-502.
[140].
35