Let S be a completely simple semigroup with a given Rees product structure A * B * C. A subsemigroup of S will be called a product subsemigroup of A * B * C if it can be represented as A' * B' * C', where A' is contained in A, B' is contained in B and C' is contained in C. Such subsemigroups appear when we look into the question of weak convergence of convolution products of (not necessarily identical) probability measures on certain topological semigroups. The reason is that the supports of tail-idempotents in the set of weak limit points of these convolution products are completely simple subsemigroups. The main result of this paper, Theorem 3.3, gives general sufficient conditions for the weak convergence of convolution products.
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机译：令S为具有给定Rees乘积结构A * B * C的完全简单半群。如果S的一个半群可以表示为A'* B'* C'，则称其为A * B * C的乘积子半群，其中A'包含在A中，B'包含在B中，C'包含在C中。当我们研究某些拓扑半群上（不一定相同）概率测度的卷积积的弱收敛问题时，会出现这种亚半群。原因是这些卷积积的弱极限点集中的尾幂等的支持是完全简单的亚半群。本文的主要结果定理3.3为卷积积的弱收敛提供了一般的充分条件。
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