Fuzzy Prokhorov metric on the set of probability measures
type: Item
instance of: scholarly article
title: Fuzzy Prokhorov metric on the set of probability measures
zbMATH Open document ID: 1225.60008
author: Aleksandr Savchenko
author: Mykhailo Zarichnyi
author: Dušan Repovš
published in: Fuzzy Sets and Systems
publication date: 2011-07-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.3884
full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary
review text: The authors consider a fuzzy analogue of the Prokhorov metric defined on the set of all probability measures of a compact fuzzy metric space. They prove that this metric induces the weak-\(*\) convergence of probability measures on a compact metrizable space. Their reason for studying the space of probability measures on fuzzy metric spaces is twofold. First, they use the property of spaces of probability measures to be absolute extensors and this allows them to solve the problem of (continuous) extension of a fuzzy metric defined on a closed subspace. The second reason to investigate the spaces of probability measures is their applicability to the theory of probabilistic systems.
reviewed by: Wolfgang Näther
Mathematics Subject Classification ID: 60A86
Mathematics Subject Classification ID: 60B99
zbMATH DE Number: 5924618
zbMATH Keywords: fuzzy metric
zbMATH Keywords: Prokhorov metric
zbMATH Keywords: probability measure
zbMATH Keywords: extension of fuzzy metrics
MaRDI profile type: Publication
OpenAlex ID: W2094109748
arXiv ID: 1105.3884
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DOI: 10.1016/J.FSS.2011.02.014
description: scientific article