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Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
197-217
Opis fizyczny
Daty
wydano
2001
Twórcy
autor
- Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
Bibliografia
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-11