Order continuous of monotone set function and convergence of measurable functions sequence

被引：47
|
作者：
Li, J [1 ]
机构：
[1] SE Univ, Dept Appl Math, Nanjing 210096, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2003年 / 135卷 / 2-3期
关键词：
fuzzy measure; order continuity; Lebesgue's theorem; fuzzy integral; monotone set function;
D O I：
10.1016/S0096-3003(01)00317-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce the concept of strongly order continuity of a set function, and use it to investigate the convergence of measurable functions sequence and of integral sequence on fuzzy measure space. Several equivalent conditions of strongly order continuity are presented. It is shown that a necessary and sufficient condition that Lebesgue's theorem remains valid for a monotone set function is that the set function possesses strongly order continuity. (C) 2002 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：211 / 218
页数：8
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