soxumis saxelmwifo universitetis S r o m e b i VII

26wherey 11 g y xg x dx .The (33) holds by virtue of the Lebesgue theorem on majorized uh g and uh 0 asconvergence and the fact that 1 ,n 2L 1. Thereby, taking (27)-(33) into account, we have proved that1au2 2 2 g du . (34)naNow let us verify the fulfillment of the conditions of the centrallimit theorems for the sumsn1Tn ajnj Ftj,nWe havesince c162Var T n .ajn 1 n1aaj11 x tKh hjg2ntx dx.2 2 2n ajnE j Fjj L n,a jn , Ft 1j12 On 2VarT nj2E for all 1 j n andFinally, the statement (b) of the theorem follows from (a) if we takeinto account thatn1aag11a1 dx n g x Ku Fx uhFxx EFˆx Fxn 1 OThe theorem is proved.Lemma 2.s2 h n h Oa n1 dudx . (35)(1) In the conditions of the item (a) of Theorem 4,s1a 217g udu, s 2ETn c . (36) a