局部紧H半群上概率测度序列的组合收敛性

Composition Convergence of Probability Measure Sequences on Locally Compact H-semigroups

首先讨论可数离散H半群上组合收敛的概率测度序列的一些极限性质,证明了相关文献中关于组合收敛必要条件的一个猜想.其次当半群具有交换性时,在同分布场合建立了强Kloss准则,证明经适当的shift变换可使概率测度卷积幂序列收敛到某个不变测度.最后讨论具有紧核的局部紧H半群上的概率测度卷积序列聚点集的构造.这些结果推广和改进了一些已有的结论.

In this paper, we first investigate some limit properties of composition convergence probability measure sequences on countable discrete H-semigroups, and verify a conjecture on the necessary condition for the composition convergence. Subsequently, in the case of being identically distributed, the strong Kloss convergence criterion on an Abelian semigroup is obtained： by suitably choosing shift transformation, a sequence of powers of probability measure convolution will converge to an invariant measure. Finally we discuss the structure of the accumulation point sets of a probability measure convolution sequence on a locally compact H-semigroup with compact kernel. All these results extend or improve the relevant results in literatures.