The Alexandroff theorem for Riesz space-valued non-additive measures

Jun Kawabe

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The Alexandroff theorem for Riesz space-valued non-additive measures

机译：Riesz空间值非可加测度的Alexandroff定理

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摘要

The Alexandroff theorem for a compact non-additive measure with values in a Riesz space is still valid for the following two cases: one is the case that the measure is autocontinuous and the Riesz space has the weak asymptotic Egoroff property and the other is the case that the measure is uniformly autocontinuous and the Riesz space is weakly σ-distributive. A close connection between regularity and continuity of non-additive measures is also given.

机译：Riesz空间中具有值的紧致非可加测度的Alexandroff定理在以下两种情况下仍然有效：一种情况是该量度是自连续的，而Riesz空间具有弱渐近Egoroff性质，另一种情况是测度是一致的自连续的，而Riesz空间是弱σ分布的。还给出了非加性测度的规律性和连续性之间的紧密联系。

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来源
《Fuzzy sets and systems》 |2007年第21期|p.2413-2421|共9页
作者
Jun Kawabe;
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作者单位

Department of Mathematics, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类模糊数学;
关键词
non-additive measure; alexandroff theorem; weak asymptotic egoroff property; multiple egoroff property; fuzzy measure; compact system; radon;

机译：非加性测度;阿兰克德罗夫定理;弱渐近的egoroff性质;多重egoroff性质;模糊测度;紧致系统;rad;

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专利

1. Regularities of Riesz space-valued non-additive measures with applications to convergence theorems for Choquet integrals [J] . Jun Kawabe Fuzzy sets and systems . 2010,第5期

机译：Riesz空间值非可加测度的正则性及其在Choquet积分收敛定理中的应用
2. The Egoroff property and the Egoroff theorem in Riesz space-valued non-additive measure theory [J] . Jun Kawabe Fuzzy sets and systems . 2007,第1期

机译：Riesz空间值非可加测度理论中的Egoroff性质和Egoroff定理
3. On sufficient conditions for the Egoroff theorem of an ordered topological vector space-valued non-additive measure [J] . Toshikazu Watanabe Fuzzy sets and systems . 2011,第1期

机译：有序拓扑向量空间值非可加测度的Egoroff定理的充分条件
4. A Study of Riesz Space-Valued Non-additive Measures [C] . Jun Kawabe Integrated uncertainty management and applications . 2010

机译：Riesz空间值非可加测度的研究
5. Three topics in analysis: (I) The fundamental theorem of calculus implies that of algebra, (II) Mini sums for the Riesz representing measure, and (III) Holomorphic domination and complex Banach manifolds similar to Stein manifolds. [D] . Mathew, Panakkal J. 2011

机译：分析中的三个主题：（I）微积分的基本定理表示代数的基本定理，（II）Riesz表示测度的最小和，以及（III）与Stein流形相似的全纯控制和复杂Banach流形。
6. ROC AND THE BOUNDS ON TAIL PROBABILITIES VIA THEOREMS OF DUBINS AND F. RIESZ [O] . Eric Clarkson, J. L. Denny, Larry Shepp -1

机译：ROC和通过Dubins和F. Riesz定理在尾部概率上的界线
7. A RIESZ TYPE REPRESENTATION THEOREM FOR RIESZ SPACE-VALUED POSITIVE LINEAR MAPPINGS (Nonlinear Analysis and Convex Analysis) [O] . Kawabe Jun 2004

机译：Riesz空间值正线性映射的Riesz型表示定理（非线性分析和凸分析）
8. Asymptotic Behavior of a System of Interacting Nuclear Space-Valued StochasticDifferential Equations Driven by Poisson Random Measures [R] . Kallianpur, G., Xiong, J. 1994

机译：poisson随机测度驱动的核空间值随机微分方程组的渐近性

The Alexandroff theorem for Riesz space-valued non-additive measures

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