On concentrated probabilities

Volume 61 / 1995

Wojciech Bartoszek Annales Polonici Mathematici 61 (1995), 25-38 DOI: 10.4064/ap-61-1-25-38


Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence $g_n ∈ G$ such that $μ^{∗n}(g_n A) ≡ 1$ for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power $μ^{∗k}$ has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological group G.


  • Wojciech Bartoszek

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