Geodesic
An Analogue of Birkhoff's Problem III for Infinite Markov Matrices1
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 625-633

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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]. 
Kim, Choo-Whan. An Analogue of Birkhoff's Problem III for Infinite Markov Matrices1. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 625-633. doi: 10.4153/CMB-1969-080-7
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     title = {An {Analogue} of {Birkhoff's} {Problem} {III} for {Infinite} {Markov} {Matrices1}},
     journal = {Canadian mathematical bulletin},
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     year = {1969},
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     doi = {10.4153/CMB-1969-080-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-080-7/}
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