LIMIT BEHAVIOURS OF CONVOLUTION SEQUENCES OF PROBABILITY MEASURES ON COMPACT ABELIAN SEMIGROUPS
紧交换半群上概率测度卷积序列的极限性质

In this paper,the method of partial groupization is applied to the study of limit behavioursof probability measures on Abelian semigroups.First the existence of the limit for the i.i.d.random variable convolution power sequence is discussed,and a result of Kawada-Ito type oncompact Abelian semigroups is given.Then,a strong principle of Kloss convergence on com-pact Abelian semigroups is set up.This principle was once obtained by Maksimov on finitgroups and compact groups.