We study the extent to which the Galvin-Mycielski-Solovay
characterization of strong measure zero subsets of the real line
extends to arbitrary Polish group. In particular, we show that
an abelian Polish group satisfies the GMS characterization if and only
if it is locally compact. We shall also consider the non-abelian case,
and discuss the use and existence of invariant submeasures on Polish groups.
(joint with W. Wohofsky, J. Zapletal and/or O. Zindulka)
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