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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Probability measures on semigroups


Author: Peter Gerl
Journal: Proc. Amer. Math. Soc. 40 (1973), 527-532
MSC: Primary 43A05; Secondary 60B15
MathSciNet review: 0318776
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Abstract: Let $ S$ be a discrete semigroup, $ P$ a probability measure on $ S$ and $ s \in S$ with $ \lim {\sup _n}{({P^{(n)}}(s))^{1/n}} = 1$. We study limit theorems for the convolution powers $ {P^{(n)}}$ of $ P$ implied by the above property and further the class of all semigroups with this property. Theorem 3 relates this class of semigroups to left amenable semigroups.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0318776-4
Keywords: Semigroup, probability measure, convolution, limit theorems, amenable semigroup
Article copyright: © Copyright 1973 American Mathematical Society