局部紧H半群上概率测度卷积幂的弱收敛性

WEAK CONVERGENCE OF CONVOLUTION POWER SEQUENCE OF PROBABILITY MEASURE ON LOCALLY COMPACT H-SEMIGROUPS

本文讨论局部紧Ｈ半群上概率测度卷积幂的弱收敛性，将紧群上的Ｋａｗａｄａ－Ｉｔｏ型结果以某种相应的形式建立到局部紧Ｈ半群上，由于紧半群上的概率测度卷积幂序列必为胎紧的，所以，不仅Ｋａｗａｄａ－Ｉｔｏ经典结果是本文的特例，而且［１］中的定理和［２］中的定理２都可以作为本文定理的推论．

in this paper, we discuss the property of the weak convergence of probability measure convolution power sequence on locally compact H semigroups. We rebuild some kind o f Kawada-Ito conclusion on locally compact H-semigroups. Because the probability measure convolution power sequence must be tight on compact semigroups. Both the Kawada-Ito classical conclusion is the example of the paper, and the Theorem in [1] and Theorem 2 in [2] are all corollaries of the Theorem in this paper.