On the heredity of Hun and Hungarian property
type: Item
instance of: scholarly article
title: On the heredity of Hun and Hungarian property
zbMATH Open document ID: 0708.60006
DOI: 10.1007/BF01046099
author: A. Zempléni
published in: Journal of Theoretical Probability
publication date: 1990-01-01T00:00:00Z
review text: 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 \(D(D(G))\), \(D(D(D(G))),\ldots\).
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 4163797
zbMATH Keywords: infinite divisibility
zbMATH Keywords: topological semigroup
zbMATH Keywords: convolution semigroup
zbMATH Keywords: Hun semigroup
zbMATH Keywords: Hungarian semigroups
zbMATH Keywords: Khinchin's decomposition theorems
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01046099
OpenAlex ID: W180601833
description: scientific article; zbMATH DE number 4163797