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.
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)
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)。
关键词
拓扑半群
概率测度
组合收敛
topological semigroup
probability measure
composition convergence
作者简介
严慧(1983-),女,湖北黄梅,讲师,主要研究方向:概率论与数理统计.
