单调度量的拉顿-尼科迪姆定理

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-05-03 DOI:10.1016/j.fss.2024.108995

Yao Ouyang , Jun Li

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引用次数: 0

摘要

证明了关于单调度量的 Choquet 积分的 Radon-Nikodym 定理的一个版本。如果ν是空连续和弱空相加的，那么f几乎在所有地方都是唯一由ν决定的，因此被称为μ关于ν的Radon-Nikodym导数。对于 σ 有限单调度量，在单调度量是下连续和空加性的假设下，也可以得到一个 Radon-Nikodym 型定理。

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A Radon-Nikodym theorem for monotone measures

A version of Radon-Nikodym theorem for the Choquet integral w.r.t. monotone measures is proved. Without any presumptive condition, we obtain a necessary and sufficient condition for the ordered pair $(μ, ν)$ of finite monotone measures to have the so-called Radon-Nikodym property related to a nonnegative measurable function f. If ν is null-continuous and weakly null-additive, then f is uniquely determined almost everywhere by ν and thus is called the Radon-Nikodym derivative of μ w.r.t. ν. For σ-finite monotone measures, a Radon-Nikodym type theorem is also obtained under the assumption that the monotone measures are lower continuous and null-additive.

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.