Cardinality and structure of extreme infinite doubly stochastic matrices (Q1293313)

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.