On an extendability problem for measures
type: Item
instance of: scholarly article
title: On an extendability problem for measures
zbMATH Open document ID: 0555.60003
DOI: 10.1007/BF01169009
author: Manfred Droste
published in: Manuscripta Mathematica
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155027
review text: The author gives a sufficient condition for the existence of extensions of probability measures from a certain class of \(\sigma\)-algebras to countable extensions of these \(\sigma\)-algebras. Then he uses this result to show: Assume that there is no measurable cardinal \(\leq 2^{\aleph_ 0}\). Then there exists a probability space (\(\Omega\),\({\mathcal A},\mu)\) such that whenever \({\mathcal B}\) is a countably generated \(\sigma\)-algebra on \(\Omega\), \(\mu\) can be extended to a measure on \(\sigma\) (\({\mathcal A}\cup {\mathcal B})\), but \(\mu\) has no extension to a measure on \({\mathcal P}(\Omega)\). This answers a question posed some years ago by C. Ryll- Nardzewski under an additional but fairly weak set-theoretic assumption in the negative.
Mathematics Subject Classification ID: 60A10
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 3885031
zbMATH Keywords: existence of extensions of probability measures
zbMATH Keywords: countably generated \(\sigma \) -algebra
MaRDI profile type: Publication
cites work: Two principles for extending probability measures
cites work: Q3852172
cites work: Extension of Measures and Stochastic Equations
cites work: Q5533187
OpenAlex ID: W2011196615
description: scientific article; zbMATH DE number 3885031