Gleichverteilung auf Diskreten Halbgruppen

Abstract

Let (μn) be a sequence of probability measures on a discrete semigroup S. In this paper we study the (left, right) uniform distribution of (μn), i.e. the vague or norm convergence of μn−δxμn→0 for every x in S δx means the point measure of x and δxμn the convolution of δx and μn). 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.