Probability measures on semigroups

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.