Haar null and non-dominating sets

• Autorzy: Sławomir Solecki
• Języki publikacji: 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.

Kategorie tematyczne

• 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
• 43A07: Means on groups, semigroups, etc.; amenable groups
• 03E15: Descriptive set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 170
• Numer: 1-2
• Strony: 197-217

Daty

wydano

2001

Twórcy

autor

Sławomir Solecki

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

Identyfikatory

DOI

10.4064/fm170-1-11