Existence of linear liftings with invariant sections in product measure spaces
type: Item
instance of: scholarly article
title: Existence of linear liftings with invariant sections in product measure spaces
zbMATH Open document ID: 1086.28003
published in: Archiv der Mathematik
publication date: 2005-02-25T00:00:00Z
review text: The authors continue their work on the relation of (measure theoretic) liftings on product measure spaces and their relations to liftings on the factor spaces. This paper deals with linear liftings which is a more general concept. In view of previous work the natural question is whether given linear liftings \(\rho, \sigma\) on the factor spaces \(\Omega_1, \Omega_2\) there is a linear lifting \(\pi\) on the product space satisfying \[ \pi (f\otimes g)= \rho (f) \otimes \sigma (g)\tag{P} \] and \[ \pi (h)_{\omega} = \sigma [\pi (h)_{\omega}] \tag{S} \] for all \( f\in L^\infty (\Omega_1), g \in L^\infty (\Omega_2), h\in L^\infty (\Omega_1 \times \Omega_2), \omega \in \Omega_1.\) They prove that the standard transfinite construction of linear liftings yields liftings \(\rho\) such that for every \(\sigma\) there is a \(\pi\) with (P) such that (S) holds for each \(h\) almost everywhere on \(\Omega_1.\)
reviewed by: Heinrich von Weizsäcker
Mathematics Subject Classification ID: 28A51
Mathematics Subject Classification ID: 28A35
Mathematics Subject Classification ID: 60A10
Mathematics Subject Classification ID: 60G05
zbMATH DE Number: 2138525
zbMATH Keywords: lifting
zbMATH Keywords: linear lifting
zbMATH Keywords: product lifting
zbMATH Keywords: product measure
zbMATH Keywords: lifting invariant sections
author: Kazimierz Musial
author: Werner Strauß
author: Nikolaos Demetrios Macheras
MaRDI profile type: Publication
full work available at URL: s00013-004-1059-2
OpenAlex ID: W2039361951
DOI: 10.1007/S00013-004-1059-2
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description: scientific article; zbMATH DE number 2138525