The class \(I_0\) on abstract structures
type: Item
instance of: scholarly article
title: The class \(I_0\) on abstract structures
zbMATH Open document ID: 0970.60016
DOI: 10.1007/BF02673721
published in: Journal of Mathematical Sciences (New York)
publication date: 2001-10-06T00:00:00Z
review text: A classical fact of the arithmetics of the semigroup of probability measures on the real line \({\mathbb R}\) is the following result of Khinchin: Every probability measure on \({\mathbb R}\) which has no indecomposable factors is infinitely divisible. Examples show that there exist infinitely divisible probability measures which have indecomposable factors. It is well-known that a large number of `reach' semigroups possess the same property: The class \(I_0\) of all elements without indecomposable factors is strictly included in the class of infinitely divisible elements of the semigroup. The authors provide three more examples: convex cones, \(q\)-probability and statistical experiments.
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1529962
zbMATH Keywords: class \(I_0\)
zbMATH Keywords: infinitely divisible elements
author: Daniel Neuenschwander
author: R. Schott
reviewed by: Alexander Ulanovskii
MaRDI profile type: Publication
cites work: Q4177796
cites work: Q5560061
cites work: Harmonic analysis of probability measures on hypergroups
cites work: Deux théoremes sur les groupes stochastiques compacts
cites work: Q4153376
cites work: On positive random objects
cites work: Infinite divisibility of random objects in locally compact positive convex cones.
cites work: Q5732991
cites work: Q4380618
full work available at URL: https://doi.org/10.1007/bf02673721
OpenAlex ID: W2062185561
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description: scientific article; zbMATH DE number 1529962