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An Analogue of Birkhoff's Problem III for Infinite Markov Matrices1

Published online by Cambridge University Press:  20 November 2018

Choo-Whan Kim
Choo-Whan Kim*
Affiliation:
Simon Fraser University
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A celebrated theorem of Birkhoff ([1], [6]) states that the set of n × n doubly stochastic matrices is identical with the convex hull of the set of n × n permutation matrices. Birkhoff [2, p. 266] proposed the problem of extending his theorem to the set of infinite doubly stochastic matrices. This problem, which is often known as Birkhoffs Problem III, was solved by Isbell ([3], [4]), Rattray and Peck [7], Kendall [5] and Révész [8].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969 , pp. 625 - 633
Copyright
Copyright © Canadian Mathematical Society 1969

Footnotes

1

This work was supported by the National Science Foundation under Grant GP-5270, Syracuse University.

References

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