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| 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． |
| 关键词: 拓扑半群 概率测度 组合收敛 |
| DOI： |
| 分类号:O211.1 |
| 基金项目:湖北省教育厅资助科研项目（D20172501；B2018148） |
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| SOME LIMIT THEOREMS OF COMPOSITION CONVERGENCE OF PROBABILITY MEASURE SEQUENCES ON TOPOLOGICAL SEMIGROUPS |
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YAN Hui,XU Li-feng,XU Kan
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| Abstract: |
| This paper investigates the composition convergence of probability measure sequence {μn} on topological semigroups, that is: the limit properties for convolution sequence μk,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. |
| Key words: topological semigroup probability measure composition convergence |
