K-拟加测度空间上Borel-Cantelli引理的局部推广  

A local generalization of Borel-Cantelli lemma on K-quasi-additive measure space

作　　者：李艳红[1] 

机构地区：[1]辽东学院师范学院数学系,辽宁丹东118000

出　　处：《东北师大学报（自然科学版）》2017年第3期29-33,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61374009)

摘　　要：基于K-拟加运算证明了集函数关于一般集合列满足次可数可加性,进而给出了K-拟加级数收敛的一个必要条件.其次,在K-拟加测度空间上获得了概率论中Borel-Cantelli引理的第一个结论,并通过构造子集合列方法对Borel-Cantelli引理进行了局部推广.The weak countable additivity of the set function is proved by means of K-quasi-additive operation for a general set sequence.A necessary condition of convergence for K-quasi-additive series is given.Meanwhile,the first conclusion of Borel-Cantelli lemma is obtained on K-quasi-additive measure space and Borel-Cantelli lemma is locally generalized by constructing a subsequence of set.

关 键 词：诱导算子 拟加法 K-拟可加测度 K-拟加级数 BOREL-CANTELLI引理 

分 类 号：O211.1[理学—概率论与数理统计]