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arXiv · 1508.02227

Naively Haar null sets in Polish groups

Márton Elekes·Zoltán Vidnyánszky
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Abstract

Let $(G,\cdot)$ be a Polish group. We say that a set $X \subset G$ is Haar null if there exists a universally measurable set $U \supset X$ and a Borel probability measure $\mu$ such that for every $g, h \in G$ we have $\mu(gUh)=0$. We call a set $X$ naively Haar null if there exists a Borel probability measure $\mu$ such that for every $g, h \in G$ we have $\mu(gXh)=0$. Generalizing a result of Elekes and Stepr\=ans, which answers the first part of Problem FC from Fremlin's list, we prove that in every abelian Polish group there exists a naively Haar null set that is not Haar null.

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BibTeXRIS

Márton Elekes, Zoltán Vidnyánszky. 2015-08-10. Naively Haar null sets in Polish groups. https://arxiv.org/abs/1508.02227

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