Haar null and non-dominating sets

Sławomir Solecki

Research output: Contribution to journalArticlepeer-review

Abstract

We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of ωω. Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain results connecting Haar null sets on countable products of locally compact Polish groups with amenability of the factor groups.

Original languageEnglish (US)
Pages (from-to)197-217
Number of pages21
JournalFundamenta Mathematicae
Volume170
Issue number1-2
DOIs
StatePublished - 2001
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory

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