Measures on product spaces and the existence of strong Baire liftings
type: Item
instance of: scholarly article
title: Measures on product spaces and the existence of strong Baire liftings
zbMATH Open document ID: 0765.28012
DOI: 10.1007/BF01572080
author: S. Grekas
author: Constantinos Gryllakis
published in: Monatshefte für Mathematik
publication date: 1993-05-12T00:00:00Z
full work available at URL: https://eudml.org/doc/178573
review text: Some notions are introduced for studying measures on product spaces, the main concept being that of property \((*)\) ``For every uncountable family \(\{V_ \alpha\}\) of open sets in \(X=\prod_{i\in I}X_ i\), where the \(V_ \alpha\) depend on pairwise disjoint sets of coordinates, we have: \(\mu(\cup_ \alpha V_ \alpha)=1\)''. In case when the topological factors are separable metric spaces, this property is equivalent to the completion regularity. We prove that \((*)\) is preserved under arbitrary products of measure spaces. As a consequence, we deduce a series of related results in measure theory (some of which are known). In particular, the following extension of a result by Losert is obtained: Subject to CH, every product of \(\leq\aleph_ 2\) many completion regular measures, each supported on any product of \(\leq\aleph_ 1\) many compact metric spaces admits a strong Baire lifting.
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 28A51
zbMATH DE Number: 164925
zbMATH Keywords: completion regular measures
zbMATH Keywords: strong Baire lifting
MaRDI profile type: Publication
cites work: Recent developments arising out of Kakutani’s work on completion regularity of measures
cites work: Products of Radon Measures: A Counter-Example
cites work: Completion regular measures on product spaces with application to the existence of Baire strong liftings
cites work: Products of Completion Regular Measures
cites work: Homeomorphic measures on products of intervals
cites work: Q5751095
cites work: Q3852172
cites work: Notes on infinite product measure spaces, I
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description: scientific article; zbMATH DE number 164925