Cardinality and structure of extreme infinite doubly stochastic matrices
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The main results of this article are contained in Sections 2 and 3. In Section 2 we show that for non-trivial infinite systems of marginals \(\cal I\) there are always continuum many extreme matrices that are doubly stochastic with respect to \(\cal I\) (cf. Theorem 2.1). Corollary 2.2 contains the corresponding result for the substochastic case. In Section 3 we show that the entries of an extreme doubly stochastic matrix are always in the closure of the additive subgroup of \(\Bbb R\) that is generated by the respective marginals (cf. Theorem 3.2). Theorem 3.4 deals with the corresponding substochastic case.
KeywordsInfinite System Stochastic Matrix Additive Subgroup Stochastic Matrice Extreme Matrice
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