A Fubini theorem

Sławomir Solecki

doi:10.1016/j.topol.2007.04.009

A Fubini theorem

Sławomir Solecki

Research output: Contribution to journal › Article › peer-review

Abstract

Let I₀ be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I₀ and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Rosłanowski-Shelah stating that I₀ on 2^N strongly violates the countable chain condition.

Original language	English (US)
Pages (from-to)	2462-2464
Number of pages	3
Journal	Topology and its Applications
Volume	154
Issue number	12
DOIs	https://doi.org/10.1016/j.topol.2007.04.009
State	Published - Jun 15 2007
Externally published	Yes

Keywords

Fubini's theorem
Haar null sets
Meager sets

ASJC Scopus subject areas

Geometry and Topology

Online availability

10.1016/j.topol.2007.04.009

Library availability

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abstract = "Let I0 be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I0 and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros{\l}anowski-Shelah stating that I0 on 2N strongly violates the countable chain condition.",

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N1 - Funding Information: Research supported by NSF grant DMS-0400931. Fax: +1 217 333 9576. E-mail address: ssolecki@math.uiuc.edu.

PY - 2007/6/15

Y1 - 2007/6/15

N2 - Let I0 be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I0 and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Rosłanowski-Shelah stating that I0 on 2N strongly violates the countable chain condition.

AB - Let I0 be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I0 and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Rosłanowski-Shelah stating that I0 on 2N strongly violates the countable chain condition.

KW - Fubini's theorem

KW - Haar null sets

KW - Meager sets

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JF - Topology and its Applications

IS - 12

ER -

A Fubini theorem

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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