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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2004 Volume 312, Pages 69–85 (Mi znsl773)

This article is cited in 64 papers

The Kantorovich metric: initial history and little-known applications

A. M. Vershik

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We remind of 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 ($\bar d$-metric), and the third one is the formulation of the strong Monge–Kantorovich problem in terms of matrix distributions.

UDC: 517.987

Received: 25.08.2004


 English version:
Journal of Mathematical Sciences (New York), 2006, 133:4, 1410–1417

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