Fuzzy measures and discreteness
type: Item
instance of: scholarly article
title: Fuzzy measures and discreteness
zbMATH Open document ID: 1164.28018
author: Congxin Wu
author: Xuekun Ren
published in: Discrete Mathematics
publication date: 2008-10-07T00:00:00Z
review text: Let \((X,\mathcal{A})\) be a measurable space and let \(\mathcal F\) be the space of real valued set functions on \(\mathcal A\) of bounded variation, i.e., \(\|\mu\| =\sup \sum_{i=1}^n |\mu(A_i)-\mu(A_{i-1})|<\infty\), where the supremum is taken over all chains \(\emptyset = A_0 \subset A_1 \subset \cdots \subset A_n = X\), \(A_i \in \mathcal{A}\). It is proved that the space \((\mathcal{F},\|\cdot\|)\) is separable if and only if the \(\sigma\)-algebra \(\mathcal A\) is finite.
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 28A33
zbMATH DE Number: 5349283
zbMATH Keywords: nonmonotonic fuzzy measure
zbMATH Keywords: Banach space
zbMATH Keywords: separability
zbMATH Keywords: \(\sigma \)-algebra
reviewed by: J. W. Hagood
MaRDI profile type: Publication
full work available at URL: j.disc.2007.09.003
OpenAlex ID: W1966729892
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DOI: 10.1016/J.DISC.2007.09.003
description: scientific article; zbMATH DE number 5349283