ON CHARACTERIZATION OF A.S. CONVERGENCE OF ALL CONDITIONINGS FOR SEQUENCES OF RANDOM VARIABLES

被引：0

作者：

Paszkiewicz, Adam ^{[1
]}

机构：

[1] Univ Lodz, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland

来源：

DEMONSTRATIO MATHEMATICA | 2012年 / 45卷 / 02期

关键词：

almost everywhere convergences; conditional expectations;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that in a non- atomic probability space, for a sequence of any integrable r.v.( X-n) we have the following equivalence: E( X-n| A)-> 0 a.s.for any sigma - field A of events iff X-n -> 0 a.s.and E sup(n) (>= 1) | Xn| < infinity

引用

页码：455 / 462

页数：8

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