The Hausdorff metric and measurable selections
type: Item
instance of: scholarly article
title: The Hausdorff metric and measurable selections
zbMATH Open document ID: 0586.28009
DOI: 10.1016/0166-8641(85)90072-0
author: C. J. Himmelberg
author: F. S. van Vleck
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: We contruct measurable selections for closed set-valued maps into arbitrary complete metric spaces. We do not need to make any separability assumptions. We view the set-valued maps as point-valued maps into the hyperspace and our measurability assumptions are the usual kinds of measurability of point-valued maps in this setting. We also discuss the relationship of these measurability conditions to the ones usually considered in the theory of measurable selections.
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54C65
zbMATH DE Number: 3939633
zbMATH Keywords: Radon measure space
zbMATH Keywords: Hausdorff metric
zbMATH Keywords: closed set-valued map
zbMATH Keywords: measurable selections
zbMATH Keywords: complete metric spaces
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90072-0
OpenAlex ID: W2082339910
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cites work: Q4148368
cites work: A new proof that analytic sets are Ramsey
cites work: Q3342807
cites work: Measurable functions and almost continuous functions
cites work: Q3952344
cites work: Q3481984
cites work: Borel Measurable Mappings for Nonseparable Metric Spaces
cites work: Hereditarily-Additive Families in Descriptive Set Theory and Borel Measurable Multimaps
cites work: Measurable relations
cites work: On measurable relation
cites work: Q4076235
cites work: On Perfect Measures
cites work: The Ramsey Property and Measurable Selections
cites work: The Measurability of Uncountable Unions
cites work: Q5541832
cites work: Q5531649
cites work: Measures in non-separable metric spaces
cites work: Q4776112
cites work: Q4108548
cites work: Survey of Measurable Selection Theorems
description: scientific article; zbMATH DE number 3939633