论文标题
紧凑型Hausdorff拓扑组的半组规则概率度量的规律性
Regularity Of The Semi-group Of Regular Probability Measures On Compact Hausdorff Topological Groups
论文作者
论文摘要
Hausdorff拓扑组G。在紧凑型/局部紧凑的常规概率度量的结构上有很多深刻的结果。众所周知，集合$ p（g）$在卷积下形成半组。温德尔在他的非凡论文中证明了支持两项概率措施的卷积的基本结果。因此，他确定半组$ p（g）$不是一个小组。在这篇简短的论文中，证明对于紧凑的拓扑组G，概率度量的半组P（g）在代数上不是定期的。但是，有一些具体的常规半组可以嵌入P（G）。
There are many deep results on the structure of REGULAR probability measures $P(G)$ on compact/locally compact, Hausdorff topological groups G. See, for instance, the classic monographs by KR Parthasarathy, Ulf Grenander, A.Mukherjea and Nicolas A.Tserpes. It is known that the set $P(G)$ forms a semi-group under convolution. Wendel in his remarkable paper, proved a basic result regarding support of convolution of two probability measures. Consequently, he established that the semi-group $P(G)$ is not a group. In this short paper, it is proved that for a compact topological group G, the semi-group P(G) of probability measures is not algebraically regular. However, there are concrete regular semi-groups in which P(G) can be embedded.
