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
收藏
页码：455 / 462
页数：8
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