关于可测函数的收敛性：两个开放问题的解

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-08-05 DOI:10.1016/j.fss.2025.109552

Do Huy Hoang , Tran Nhat Luan

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引用次数: 0

摘要

在本文中，我们给出了由Hutník提出的“基于最小半大众的通用积分II：收敛定理”（Fuzzy Sets and Systems 271(2015), 18-30）中开放问题2.18和2.19的解。证明了当且仅当底层单调测度为零测度时，严格的测度收敛等价于测度收敛和均值收敛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the convergence of measurable functions: Solutions to two open problems

In this paper, we provide solutions of open problems 2.18 and 2.19 in the paper “The smallest semicopula-based universal integrals II: Convergence theorems” (Fuzzy Sets and Systems 271(2015), 18-30) which were posed by Hutník. It is shown that strict convergence in measure is equivalent to convergence in measure and convergence in mean if and only if the underlying monotone measure is the zero measure.

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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.