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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2001 | 170 | 1-2 | 197-217

## Haar null and non-dominating sets

EN

### Abstrakty

EN
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 $ω^{ω}$. 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.

197-217

wydano
2001

### Twórcy

autor
• Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.