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arXiv · 1006.2675

The Steinhaus property and Haar-null sets

Pandelis Dodos
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Abstract

It is shown that if $G$ is an uncountable Polish group and $A\subseteq G$ is a universally measurable set such that $A^{-1}A$ is meager, then the set $T_l(A)=\{μ\in P(G): μ(gA)=0 \text{for all} g\in G\}$ is co-meager. In particular, if $A$ is analytic and not left Haar-null, then $1\in\mathrm{Int}(A^{-1}AA^{-1}A)$.

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Pandelis Dodos. 2010-06-14. The Steinhaus property and Haar-null sets. https://doi.org/10.1112/blms%2Fbdp014

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