A Yosida-Hewitt decomposition for minitive set functions
type: Item
instance of: scholarly article
title: A Yosida-Hewitt decomposition for minitive set functions
zbMATH Open document ID: 1087.28008
author: Yann Rébillé
published in: Fuzzy Sets and Systems
publication date: 2006-01-24T00:00:00Z
review text: A set function \(\nu:{\mathfrak A}\to \mathbb{R}\) on a \(\sigma\)-algebra is called minitive if \(\nu(A\cap B)= \min\{\nu(A), \nu(B)\}\) for all \(A,B\in{\mathfrak A}\). The author proves that a minitive set function has a unique decomposition of the form \(\nu= \nu_c+ \nu_p\) where \(\nu_c\) is \(\sigma\)-continuous and \(\nu_p\) is pure. If \({\mathfrak A}= \mathbb{P}(\mathbb{N})\), a precise description of \(\nu_c\) is given.
reviewed by: Hans Weber
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 5001383
zbMATH Keywords: fuzzy minitive measures
zbMATH Keywords: Hewitt-Yosida decomposition
zbMATH Keywords: necessity measures
zbMATH Keywords: Choquet integral
MaRDI profile type: Publication
full work available at URL: j.fss.2005.06.012
OpenAlex ID: W2079980072
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DOI: 10.1016/J.FSS.2005.06.012
description: scientific article; zbMATH DE number 5001383