Cardinality and structure of extreme infinite doubly stochastic matrices
type: Item
instance of: scholarly article
title: Cardinality and structure of extreme infinite doubly stochastic matrices
zbMATH Open document ID: 0930.15024
author: Peter Philip
published in: Archiv der Mathematik
publication date: 2000-02-16T00:00:00Z
review text: The main results of this article are in Section 2 and 3. In Section 2 the author shows that for nontrivial infinite systems of marginals \(T\) there are continuum many extreme matrices that are doubly stochastic with respect to \(T\). Corollary 2.2 contains the corresponding result for the substochastic case. In Section 3 the author shows that the entries of an extreme doubly stochastic matrix are in the closure of the additive subgroup of \(R\) that is generated by the respective marginals. Theorem 3.4 deals with the corresponding substochastic case.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15B51
zbMATH DE Number: 1309638
zbMATH Keywords: extreme infinite doubly stochastic matrices
zbMATH Keywords: infinite systems of marginals
zbMATH Keywords: extreme matrices
zbMATH Keywords: additive subgroup
MaRDI profile type: Publication
full work available at URL: s000130050285
OpenAlex ID: W1978124298
DOI: 10.1007/S000130050285
description: scientific article; zbMATH DE number 1309638