Convergence of a sequence of weakly regular set functions
type: Item
instance of: scholarly article
title: Convergence of a sequence of weakly regular set functions
zbMATH Open document ID: 0947.28004
DOI: 10.1007/BF02356068
author: V. M. Klimkin
author: T. A. Sribnaya
published in: Mathematical Notes
publication date: 2000-11-01T00:00:00Z
review text: J. Dieudonné proved that if a sequence of regular Borelian measures converges on the system of open subsets of a compact metric space \(X\), then it converges on all Borelian subsets of \(X\). This theorem has been generalized by many authors, e.g., by A. Grothendieck (for \(X\) being locally compact) or by P.~Gänssler (for a regular Hausdorff space \(X\)). In this paper the authors prove an analogous theorem for set functions that are weakly regular, non-additive, defined on some algebra of sets which contains the class of open subsets of an arbitrary \(\sigma\)-topological space \(X\), and take values in a uniform space.
reviewed by: Tomasz Natkaniec
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 28A10
Mathematics Subject Classification ID: 28B20
zbMATH DE Number: 1256797
zbMATH Keywords: Borelian measure
zbMATH Keywords: set function
zbMATH Keywords: \(\sigma\)-topological space
zbMATH Keywords: Dieudonné theorem
MaRDI profile type: Publication
cites work: Q5805269
cites work: Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K)
cites work: Q5784248
cites work: Boundedness of vector-valued exterior measures
cites work: Q4138969
cites work: Q4731410
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description: scientific article; zbMATH DE number 1256797