Gleichverteilung auf Diskreten Halbgruppen

Let (μ_n) be a sequence of probability measures on a discrete semigroup S. In this paper we study the (left, right) uniform distribution of (μ_n), i.e. the vague or norm convergence of μ_n−δ_xμ_n→0 for every x in S δ_x means the point measure of x and δ_xμ_n the convolution of δ_x and μ_n). We shall give equivalent conditions for the (left, right) uniform distributed sequences and relate the existence of such sequences to the (left, right) amenable semigroups. In the last section we consider especially the uniform distribution of the convolution sequence μⁿ of a probability measure.