A further investigation for fuzzy measures on metric spaces
type: Item
instance of: scholarly article
title: A further investigation for fuzzy measures on metric spaces
zbMATH Open document ID: 0954.28009
DOI: 10.1016/S0165-0114(98)00328-5
author: Qingshan Jiang
author: Shengrui Wang
author: Djemel Ziou
published in: Fuzzy Sets and Systems
publication date: 1999-09-22T00:00:00Z
review text: A set function \(m: B\to [0,\infty]\) defined on the family of all Borel subsets of a metric space is an LSC-fuzzy measure if \(m(\emptyset)=0\), \(m\) is monotone and continuous from below. It is said to be exhaustive if \(\lim m(E_n)= 0\) for any disjoint sequence \((E_n)\). It is said to have the pseudometric generating property if, for any \(\varepsilon> 0\), there exists \(\delta>0\) such that \(m(E\cup F)< \varepsilon\) whenever \(m(E)< \delta\) and \(m(F)<\delta\). In the paper the Egorov and Luzin theorems are proved in the case that there is given an LSC-fuzzy measure that is exhaustive and has the pseudometric generating property.
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 1339628
zbMATH Keywords: Egoroff's theorem
zbMATH Keywords: Lusin's theorem
zbMATH Keywords: autocontinuity
zbMATH Keywords: exhaustivity
zbMATH Keywords: regularity
zbMATH Keywords: LSC-fuzzy measure
zbMATH Keywords: pseudometric generating property
MaRDI profile type: Publication
cites work: Some notes on the regularity of fuzzy measures on metric spaces
cites work: Fuzzy measures on metric spaces
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cites work: Q5533878
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full work available at URL: s0165-0114(98)00328-5
OpenAlex ID: W1990596074
description: scientific article; zbMATH DE number 1339628