Displaying similar documents to “Cardinal characteristics of the ideal of Haar null sets”

Haar null and non-dominating sets

Sławomir Solecki (2001)

Fundamenta Mathematicae

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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....

A note on the intersection ideal ℳ ∩ 𝒩

Tomasz Weiss (2013)

Commentationes Mathematicae Universitatis Carolinae

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We prove among other theorems that it is consistent with Z F C that there exists a set X ⊆ 2 ω which is not meager additive, yet it satisfies the following property: for each F σ measure zero set F , X + F belongs to the intersection ideal ℳ ∩ 𝒩 .

On concentrated probabilities on non locally compact groups

Wojciech Bartoszek (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let G be a Polish group with an invariant metric. We characterize those probability measures μ on G so that there exist a sequence g n ∈ G and a compact set A ⊆ G with   μ * n ( g n A ) ≡ 1   for all n .

A remark on a theorem of Solecki

Petr Holický, Luděk Zajíček, Miroslav Zelený (2005)

Commentationes Mathematicae Universitatis Carolinae

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S. Solecki proved that if ℱ is a system of closed subsets of a complete separable metric space X , then each Suslin set S ⊂ X which cannot be covered by countably many members of ℱ contains a G δ set which cannot be covered by countably many members of ℱ . We show that the assumption of separability of X cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the σ -ideal generated by ℱ is locally determined. Using Solecki’s arguments, our result...