The Egoroff theorem for non-additive measures in Riesz spaces

被引：17
作者：
Kawabe, Jun [1 ]
机构：
[1] Shinshu Univ, Fac Engn, Dept Math, Nagano 3808553, Japan
来源：
FUZZY SETS AND SYSTEMS | 2006年 / 157卷 / 20期
关键词：
non-additive measures; Riesz space; the Egoroff condition; the asymptotic Egoroff property;
D O I：
10.1016/j.fss.2006.06.014
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The Egoroff theorem remains valid for any Riesz space-valued non-additive measure which is continuous from above and below by assuming that the Riesz space has the asymptotic Egoroff property. This property is satisfied for many concrete Riesz spaces, such as R-S of all real functions on a non-empty set S, L-0[0, 1] of all Lebesgue measurable functions, and their ideals. (C) 2006 Elsevier B.V. All rights reserved.
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收藏
页码：2762 / 2770
页数：9
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