Metrizability and paracompactness of probability measure spaces
type: Item
instance of: scholarly article
title: Metrizability and paracompactness of probability measure spaces
zbMATH Open document ID: 0823.54007
author: Yusef Al'Kassas
published in: Moscow University Mathematics Bulletin
publication date: 1995-08-14T00:00:00Z
review text: Let \(P(X)\) be the family of probability measures on Tikhonov space \(X\) [\textit{V. V. Fedorchuk}, Russ. Math. Surv. 46, No. 1, 45-93 (1991); translation from Usp. Mat. Nauk 46, No. 1(227), 41-80 (1991; Zbl 0735.54033)]. The author proves that if \(X\) is metrizable, then \(P(X)\) is also metrizable. Furthermore, if \(X\) is \(p\)-paracompact, then \(P(X)\) is also \(p\)-paracompact. The author gives a characterization of absolute retracts of a metrizable space \(X\) in terms of some convex subsets of \(P(X)\).
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 60B05
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 54E45
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 54C15
zbMATH DE Number: 732060
zbMATH Keywords: paracompact space
zbMATH Keywords: probability measures
zbMATH Keywords: absolute retracts of a metrizable space
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 732060