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

作　　者：严慧 徐立峰 徐侃 YAN Hui;XU Lifeng;XU Kan(School of Mathematics and Statistics,Hubei Normal University,Huangshi,Hubei,335002,P.R China)

机构地区：[1]湖北师范大学数学与统计学院,黄石湖北435002

出　　处：《数学进展》2018年第5期791-800,共10页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11471105);湖北省教育厅重点科研项目(Nos.D20172501;B20182202)

摘　　要：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.

关 键 词：拓扑半群 概率测度 组合收敛 不变测度 

分 类 号：O211.1[理学—概率论与数理统计]