Strassen disintegration theorems
type: Item
instance of: scholarly article
title: Strassen disintegration theorems
zbMATH Open document ID: 0870.47026
DOI: 10.1007/BF01195542
author: Peter Meyer-Nieberg
published in: Archiv der Mathematik
publication date: 1997-09-15T00:00:00Z
review text: The scalar valued disintegration theorem states that for a real vector space \(X\) and a measure space, if a linear functional \(\varphi\) on \(X\) has the property that \(\varphi(x)\) is dominated by \(\int{\mathfrak D}(x)d\mu\) for all \(x\) in \(X\) where \({\mathfrak D}\) is a sublinear operator from \(X\) into \(L^1(\mu)\), then there exists a linear operator \(T\) dominated by \({\mathfrak D}\) from \(X\) into \(L^1(\mu)\) so that \(\varphi(x)=\int T(x)d\mu\). \textit{M. Neumann} [Arch. Math. 29, 413-420 (1977; Zbl 0368.28013)] provided a generalization of this result. Here a more general version, not dependent on the Radon-Nikodym property, is provided in the setting of Riesz spaces. Several consequences of this generalization are considered.
reviewed by: William A. Feldman
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 815695
zbMATH Keywords: scalar valued disintegration theorem
zbMATH Keywords: sublinear operator
zbMATH Keywords: dominated
zbMATH Keywords: not dependent on the Radon-Nikodym property
zbMATH Keywords: Riesz spaces
MaRDI profile type: Publication
cites work: Q4148368
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description: scientific article; zbMATH DE number 815695