# Article

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Keywords:
concentration function; random walk; Markov operator; invariant measure
Summary:
Let $G$ be a Polish group with an invariant metric. We characterize those probability measures $\mu$ on $G$ so that there exist a sequence $g_n \in G$ and a compact set $A \subseteq G$ with \, ${\mu}^{*n} (g_n A) \equiv 1$ \, for all $n$.
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