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A note on intersections of non-Haar null sets

Eva Matoušková, Miroslav Zelený (2003)

Colloquium Mathematicae

We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.

Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic

Karim Khanaki (2016)

Fundamenta Mathematicae

This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup such as amenability and the fixed point on compacta property. Second, we define types and develop local stability in the framework of integral logic. For a stable formula ϕ, we prove definability of all complete ϕ-types over models and deduce from this the fundamental...

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