On dense univalued representations of multivalued maps
type: Item
instance of: scholarly article
title: On dense univalued representations of multivalued maps
zbMATH Open document ID: 0581.28006
DOI: 10.1007/BF02844498
publication date: 1984-01-01T00:00:00Z
review text: Let \(\Gamma\) be a measurable multifunction whose domain is a probability space \(\Omega\) and whose values are non-empty closed subsets of a Polish space X. Write \({\mathcal F}\) for the collection of (single-valued) measurable functions from \(\Omega\) to X, and \({\mathcal F}_{\Gamma}\) for the collection of functions in \({\mathcal F}\) which are selectors for \(\Gamma\). The author describes two pseudo-metric topologies on \({\mathcal F}\) with the property that if \(\{f_ n\}\) is dense in \({\mathcal F}_{\Gamma}\), then \(\{f_ n(\omega)\}\) is dense in \(\Gamma\) (\(\omega)\) for almost all \(\omega\in \Omega\).
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 3929355
zbMATH Keywords: convergence in the space of multifunctions
zbMATH Keywords: Castaing representation of a multifunction
zbMATH Keywords: convergence in measure
zbMATH Keywords: convergence in distribution
zbMATH Keywords: measurable multifunction
zbMATH Keywords: selectors
reviewed by: Edward A. Azoff
MaRDI profile type: Publication
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author: Zvi Artstein
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 3929355