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Archiv der Mathematik

, Volume 71, Issue 5, pp 417–424 | Cite as

Cardinality and structure of extreme infinite doubly stochastic matrices

  • Peter Philip
Article

Abstract.

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.

Keywords

Infinite System Stochastic Matrix Additive Subgroup Stochastic Matrice Extreme Matrice 

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Peter Philip
    • 1
  1. 1.Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2 - 6, D-14195 Berlin, GermanyDeutschland

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