Regularity and Lusin's theorem for Riesz space-valued fuzzy measures
type: Item
instance of: scholarly article
title: Regularity and Lusin's theorem for Riesz space-valued fuzzy measures
zbMATH Open document ID: 1121.28021
author: Jun Kawabe
published in: Fuzzy Sets and Systems
publication date: 2007-05-04T00:00:00Z
review text: In non-additive measure theory, \textit{J. Li} and \textit{M. Yasuda} [Fuzzy Sets Syst. 146, No. 1, 121--133 (2004; Zbl 1046.28012)] proved that every weakly null-additive fuzzy Borel measure on a metric space is regular and Lusin's theorem remains valid for such non-additive measures. The purpose of this paper is to extend those results to Riesz space-valued fuzzy measures. Instead of epsilon-argument, a smoothness condition (the multiple Egoroff property) on a Riesz space is introduced and imposed to show this regularity property. Then, by using this regularity and Egoroff's theorem, it is also proved that Lusin's theorem remains valid.
reviewed by: Wolfgang Näther
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 5149486
zbMATH Keywords: Non-additive measures
zbMATH Keywords: multiple Egoroff property
zbMATH Keywords: regularity of non-additive measures
MaRDI profile type: Publication
full work available at URL: j.fss.2006.12.010
OpenAlex ID: W2060935534
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DOI: 10.1016/J.FSS.2006.12.010
description: scientific article; zbMATH DE number 5149486