On nonmeasurable unions

For a Polish space X and a σ-ideal I of subsets of X which has a Borel base we consider families A of sets in I with the union ⋃ A not in I. We determine several conditions on A which imply the existence of a subfamily A ′ of A whose union ⋃ A ′ is not in the σ-field generated by the Borel sets on X...

Full description

Saved in:
Bibliographic Details
Published inTopology and its applications Vol. 154; no. 4; pp. 884 - 893
Main Authors Cichoń, Jacek, Morayne, Michał, Rałowski, Robert, Ryll-Nardzewski, Czesław, Żeberski, Szymon
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.02.2007
Subjects
Algebraic sum
Baire property
Cantor set
Lebesgue measure
secondary
Lebesgue measure
Cantor set
Algebraic sum
Baire property
primary
Online AccessGet full text

Cover

More Information
Summary:For a Polish space X and a σ-ideal I of subsets of X which has a Borel base we consider families A of sets in I with the union ⋃ A not in I. We determine several conditions on A which imply the existence of a subfamily A ′ of A whose union ⋃ A ′ is not in the σ-field generated by the Borel sets on X and I. Main examples are X = R and I being the ideal of sets of Lebesgue measure zero or the ideal of sets of the first Baire category.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2006.09.013