有限Hausdorff拓扑半群上概率测度卷积序列的弱收敛性

WEAK CONVERGENCE OF CONVOLUTION SEQUENCES OF PROBABILITY MEASURES ON A FINITE HAUSDORFF TOPLOGICAI SEMIGROUP

在非同分布场合下,拓扑群(半群)上随机变量卷积序列极限存在的充要条件是一个至今尚未得到解决的问题,但是在有限群时[1]得到一些重要结果,本文的主要目的是将[1]中的定理1,定理2推广到一类有限半群上。

Let S be a fimite semigroup with idendity e, H be asubgroup of S, e∈H {μn }n be a seguence of Paobability weasures on S Wj be Haar measure on H. then We have:In Order that {μn}n>1 strang c omposidion converge to WH it ishecessary ana sufficient that μi (H) 0 beginning with some J0end the seguence { σa } n 1 strong composition converge to Wi, where for every Borel set BThis is an extension of Thl and Thz in [1]