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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Birkhoff, G., Tres observaciones sobre el algebra lineal. Rev. Univ. nac. Tucuman A. 5 (1946) 147–151. Google Scholar

[2] 2. Birkhoff, G., Lattice theory (revised edition). (New York, 1948). Google Scholar

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[7] 7. Rattray, B.A. and Peck, J. E. L., Infinite doubly stochasticmatrices. Trans. Roy. Soc. Canada III (3) 49 (1955) 55–57. Google Scholar

[8] 8. Revesz, P., A probabilistic solution of P roblem 111 of G. Birkhoff. Acta. Math. Acad. Sci. Hungar. 13 (1962) 187–198. Google Scholar

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