Extending Lebesgue measure by infinitely many sets
type: Item
instance of: scholarly article
title: Extending Lebesgue measure by infinitely many sets
zbMATH Open document ID: 0582.28004
author: Tim Carlson
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Consider the following question: under what conditions on a collection of subsets of the unit interval can the existence of an extension of Lebesgue measure defined on each element of the collection be guaranteed? The main purpose of this paper is to find conditions on the cardinality of the collection whose sufficiency can be shown consistent without the use of large cardinals. For example, if ZFC is consistent so is ZFC \(+ ''Lebesgue\) measure can be extended to any countable collection of sets''. - The results of this paper complement work of earlier researchers. Banach and Kuratowski showed that assuming the continuum hypothesis there is a countable collection of sets of reals for which no extension exists. Solovay proved that an extension of Lebesgue measure to all sets is equiconsistent with the existence of a measurable cardinal.
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 3931324
zbMATH Keywords: extension of Lebesgue measure
zbMATH Keywords: countable collection of sets of reals
MaRDI profile type: Publication
full work available at URL: pjm.1984.115.33
OpenAlex ID: W2041668012
DOI: 10.2140/PJM.1984.115.33
description: scientific article; zbMATH DE number 3931324