拓扑半群上概率测度序列组合收敛性的若干极限定理  

SOME LIMIT THEOREMS OF COMPOSITION CONVERGENCE OF PROBABILITY MEASURE SEQUENCES ON TOPOLOGICAL SEMIGROUPS

作　　者：严慧 徐立峰 徐侃 YAN Hui;XU Li-feng;XU Kan(School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《数学杂志》2020年第3期354-362,共9页Journal of Mathematics

基　　金：湖北省教育厅资助科研项目(D20172501,B2018148)。

摘　　要：本文研究了拓扑半群上概率测度序列{μn}的组合收敛性,即卷积序列μk,n:=μk+1*μk+2*…*μn的极限性质.通过对概率测度支撑集代数结构的研究,首先得到可数离散半群上概率测度序列组合收敛的一个充分条件,它推广了经典的Marksimov定理,也推广和改进了文献中已有的一些结果.其次给出了局部紧H半群上概率测度卷积序列{μk,n:0≤k<n}极限点集的一个构造定理,它是群上经典结果在这类半群上的推广。This paper investigates the composition convergence of probability measure sequence{μn}on topological semigroups,that is:the limit properties for convolution sequenceμk,n:=μk+1*μk+2*…*μn.By studying the algebraic construction of probability measure support,first,a sufficient criterion of composition convergence for probability measures sequences on a countable discrete semigroup is presented,which expend the classical Maksimov theorem and some other results in references.Second,we give a constructive theorem of limit point set of convolution sequences{μk,n:0≤k<n}on a locally compact H semigroup with a compact kernel,which is an extension of classical result on groups.

关 键 词：拓扑半群 概率测度 组合收敛 

分 类 号：O211.1[理学—概率论与数理统计]