Abstract
We remind of the history of the transportation (Kantorovich) metric and the Monge-Kantorovich problem. We also describe several little-known applications: the first one concerns the theory of decreasing sequences of partitions (tower of measures and iterated metric), the second one relates to Ornstein's theory of Bernoulli automorphisms (d¯-metric), and the third one is the formulation of the strong Monge-Kantorovich problem in terms of matrix distributions. Bibliography: 29 titles
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 69–85.
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Vershik, A.M. Kantorovich Metric: Initial History and Little-Known Applications. J Math Sci 133, 1410–1417 (2006). https://doi.org/10.1007/s10958-006-0056-3
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DOI: https://doi.org/10.1007/s10958-006-0056-3