The Steinhaus property and Haar-null sets

Details The Steinhaus property and Haar-null sets The Steinhaus property and Haar-null sets

2010-06-14

arxiv.org/abs/1006.2675v1

Bulletin of the London Mathematical Society 41 (2009), 377-384

Mathematics

Functional Analysis

9 pages, no figures

Scientific paper

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
$T_l(A)=\{\mu\in P(G): \mu(gA)=0 \text{for all} g\in G\}$ 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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