Probability measures on semigroups

Abstract

Let S S be a discrete semigroup, P P a probability measure on S S and s ∈ S s \in S with lim sup n ( P ( n ) ( s ) ) 1 / n = 1 \lim {\sup _n}{({P^{(n)}}(s))^{1/n}} = 1 . We study limit theorems for the convolution powers P ( n ) {P^{(n)}} of P 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.