Subsemigroups of completely simple semigroups and weak convergence of convolution products of probability measures (Q1882655)

Let \(S\) be a completely simple semigroup with a given Rees product structure \(A\times B\times C\). A subsemigroup of \(S\) is called a product subsemigroup if it can be represented in a way compatible with the product structure. The authors give conditions under which a subsemigroup of \(S\) is such a product subsemigroup. The area of application of these results is the analysis of convolution products of (nonidentical) probability measures on \(S\) and their so-called tail idempotents. It is well-known that the support of an idempotent probability measure is a completely simple semigroup. The main result of the paper gives sufficient conditions for the weak convergence of a convolution sequence of probability measures on \(S\).