Limits of Convolution Sequences of Measures on a Compact Topological Semigroup
Limits of Convolution Sequences of Measures on a Compact Topological Semigroup
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紧拓扑半群上测度卷积序列的极限
DOI：
10.1512/iumj.1960.9.59017
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发表时间：
1960
影响因子：
1.1
通讯作者：
M. Rosenblatt
中科院分区：
文献类型：
--
作者：
M. Rosenblatt
导论.研究了紧拓扑半群上正则测度的卷积序列的极限性质。KAWADA和ITO [4]研究了紧群中出现的类似问题，最近BELLMAN [1]和GRENANDER [3]考虑了独立同分布随机算子乘积的特殊极限定理。这些问题与本文所讨论的问题密切相关。应该注意的是，当考虑平稳随机过程的结构时，也会出现类似的问题[7]。紧半群上的各种结果被用来刻画极限测度类[5]，[6]，[8]。
Introduction. Limit properties of the convolution sequence of a regular measure on a compact topological semigroup are examined in this paper. Similar questions, as they arise in the case of a compact group, were examined byKAWADA & ITO [4], Recently BELLMAN [1] and GRENANDER [3] considered special limit theorems for products of independent identically distributed random operators. Such problems are closely related to those in this paper. It should be noted that similar questions arise when considering the structure of stationary stochastic processes [7]. Various results on compact semigroups are used in characterizing the class of limit measures [5], [6], [8].