Kurzweil-Henstock Integral in Riesz spaces - Bentham Science

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Kurzweil-Henstock Integral in Riesz spaces Antonio Boccuto Beloslav Riean Marta Vrábelová 2009
CONTENTS Foreword i Preface ii Contributors iv 1. Elementary Introduction to Kurzweil-Henstock Integral 1 1.1 Introduction 1 1.2 Definition of Kurzweil-Henstock integral 3 1.3 Basic theorems 6 1.4 Continuity of the integral 9 1.5 Fundamental theorem of calculus 10 1.6 Improper integrals 12 1.7 Absolute integrability 14 1.8 Convergence theorems 18 1.9 Unbounded intervals 23 2 Elementary Theory of Riesz Spaces 25 2.1 Lattice ordered groups 25 2.2 Weak σ-distributivity 29 2.3 Riesz spaces 36 3 Kurzweil - Henstock Integral with Values in Riesz Spaces 42 3.1 Definition and elementary properties 42 3.2 Uniform convergence theorem 48 3.3 Kurzweil - Stieltjes integral 49 4 Double Integrals 52 4.1 Definition of the double integral 52 4.2 Double integral of continuous functions 56 4.3 Compound partitions 59 4.4 Fubini’s theorem 60 5 Kurzweil - Henstock Integral in Topological Spaces 62 5.1 Elementary properties 62 5.2 Monotone convergence theorem 66 6 Convergence Theorems 71 6.1 Elementary properties 71 6.2 General convergence theorems 74 6.3 Henstock lemma 76 6.4 Levi’s theorem 77 6.5 Lebesgue’s theorem 80
Page 4 and 5: 7 Improper Integral 84 7.1 Real val
Page 6 and 7: ii PREFACE Kurzweil and Henstock’
Page 8 and 9: iv KURZWEIL-HENSTOCK INTEGRAL IN RI
Page 10 and 11: 2 Kurzweil-Henstock Integral in Rie
Page 12 and 13: Kurzweil-Henstock Integral in Riesz
Page 14 and 15: Elementary Theory of Riesz Spaces K
Page 16 and 17: Kurzweil-Henstock Integral with Val
Page 18 and 19: 52 Kurzweil-Henstock Integral in Ri
Page 20 and 21: 54 Kurzweil-Henstock Integral in Ri
Page 22 and 23: Kurzweil-Henstock Integral in Topol
Page 24 and 25: 6 Convergence Theorems Kurzweil-Hen
Page 26 and 27: Convergence Theorems Kurzweil-Henst
Page 28 and 29: Improper Integral Kurzweil-Henstock
Page 30 and 31: 8 Choquet and ipo Integrals Kurzwei
Page 32 and 33: Choquet and ipo Integrals Kurzweil-
Page 34 and 35: (SL)-Integral Kurzweil-Henstock Int
Page 36 and 37: 166 Kurzweil-Henstock Integral in R
Page 38 and 39: 168 Kurzweil-Henstock Integral in R
Page 40 and 41: Applications in Multivalued Logic K
Page 44 and 45: Applications in Probability Theory
Page 46 and 47: Integration in Metric Semigroups Ku
Page 50 and 51: References Kurzweil-Henstock Integr
Page 52 and 53:
Index Kurzweil-Henstock Integral in
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Kurzweil-Henstock Integral in Riesz spaces - Bentham Science

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