On the heredity of Hun and Hungarian property
Let \(S\) be a topological semigroup, \(D(S)\) the convolution semigroup of compact-regular probability measures on \(S\). \textit{I. Z. Ruzsa} and \textit{G. J. Székely} [Algebraic probability theory. Chichester (UK): Wiley (1988; Zbl 0653.60012)] extended Hinčin's classical decomposition theorems from \(D(R)\) to a large class of semigroups, called Hun and Hungarian. The author of this paper answers some of the open problems posed in this book. It is proved that if \(S\) is a stable, completely regular Hun semigroup then \(D(S)\) is also stable and Hun. (This result can be applied to finite point processes.) A similar theorem is proved for Hungarian semigroups. Thus if \(G\) is a locally compact Hausdorff group then Hinčin's decomposition theorems can be extended to \(D(D(G))\), \(D(D(D(G))),\ldots\).
scientific article; zbMATH DE number 4163797