The Steinhaus property and Haar-null sets
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 $T_l(A)=\{\mu\in P(G): \mu(gA)=0 \text{for all} g\in G\}$ is co-meager. In particular, if $A$ is analytic and not left Haar-null, then $1\in\mathrm{Int}(A^{-1}AA^{-1}A)$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2010
- DOI:
- 10.48550/arXiv.1006.2675
- arXiv:
- arXiv:1006.2675
- Bibcode:
- 2010arXiv1006.2675D
- Keywords:
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- Mathematics - Functional Analysis
- E-Print:
- 9 pages, no figures