紧拓扑半群上概率测度卷积序列的极限性质

本文讨论紧拓扑半群上概率测度卷积序列的若干重要极限性质．在第１节中，我们讨论测度集的代数结构与其支撑集代数结构的关系．第２节的定理１，通过支撑集的代数结构给出组合收敛测度序列的一个极限定理．在定理２中我们讨论独立同分布时的情形，建立了一类紧半群上的Ｋａｗａｄａ－Ｉｔ型结果．这些定理推广了紧群、紧交换半群、紧Ｌ－Ｘ半群上一些相应的结论．

Limit Behaviors of Convolution Sequences of Probability Measures on Compact Topological Semigroups

In this paper we discuss some important limit behaviors of convolution sequences of probability measures on compact semigroups.In Theorem 1,we use the algebra structure of the support of probability measures to give a limit theorem for composition convergent sequence.In Theorem 2, we discuss the i.i.d random variable convolution power sequences and a result of Kawada-It type is set up on some compact semigroups.Some results on compact groups,compact commutative semigroups,compact L-X semigroups are extended.