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Bulletin of the London Mathematical Society Advance Access originally published online on March 11, 2009
Bulletin of the London Mathematical Society 2009 41(2):377-384; doi:10.1112/blms/bdp014
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© 2009 London Mathematical Society

The Steinhaus property and Haar-null sets

Pandelis Dodos

Department of Mathematics
Texas A&M University
3368 TAMU
College Station, TX 77843-3368
USA

Received 20 November 2007. Revision received 3 November 2008.

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

2000 Mathematics Subject Classification 54H11, 28C10.


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