On Dieudonné's boundedness theorem
type: Item
instance of: scholarly article
title: On Dieudonné's boundedness theorem
zbMATH Open document ID: 0697.28004
DOI: 10.1016/0022-247X(90)90412-9
author: Emma Guariglia
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The author proves a version of Dieudonné's boundedness theorem for group-valued finitely additive regular set functions defined on a field \({\mathfrak U}\). Regularity is defined with respect to two sublattices \({\mathfrak F}\) and \({\mathfrak G}\) of \({\mathfrak U}\), which satisfy certain conditions and correspond in a topological setting to the systems of closed and open sets, respectively. In the special case of \({\mathfrak F}={\mathfrak G}={\mathfrak U}\) one gets Nikodým's boundedness theorem for set functions defined on an algebra satisfying the ``subsequential interpolation property''.
Mathematics Subject Classification ID: 28B10
zbMATH DE Number: 4142369
zbMATH Keywords: regular measures
zbMATH Keywords: uniform boundedness
zbMATH Keywords: Dieudonné's boundedness theorem
zbMATH Keywords: group-valued finitely additive regular set functions
zbMATH Keywords: Nikodým's boundedness theorem
zbMATH Keywords: subsequential interpolation property
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4142369