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The Kantorovich metric: the initial history and little-known applications. (English. Russian original) Zbl 1090.28009
J. Math. Sci., New York 133, No. 4, 1410-1417 (2006); translation from Zap. Nauchn. Semin. POMI 312, 69-85, 311 (2004).
Summary: We remind on the history of the transportation metric (Kantorovich metric) and the Monge-Kantorovich problem. We 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 concerns Ornstein’s theory of Bernoulli automorphisms $$(\overline d$$-metric), and the third one is the formulation of the strong Monge-Kantorovich problem in terms of matrix distributions.

##### MSC:
 28D05 Measure-preserving transformations 01A60 History of mathematics in the 20th century 49Q20 Variational problems in a geometric measure-theoretic setting
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