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 language | English (US) |
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Pages (from-to) | 197-217 |
Number of pages | 21 |
Journal | Fundamenta Mathematicae |
Volume | 170 |
Issue number | 1-2 |
DOIs | |
State | Published - 2001 |
Externally published | Yes |
ASJC Scopus subject areas
- Algebra and Number Theory