Geodesic
The Kantorovich metric: initial history and little-known applications
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part XI, Tome 312 (2004), pp. 69-85

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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. 
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     author = {A. M. Vershik},
     title = {The {Kantorovich} metric: initial history and little-known applications},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {69--85},
     publisher = {mathdoc},
     volume = {312},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_312_a8/}
}
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A. M. Vershik. The Kantorovich metric: initial history and little-known applications. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part XI, Tome 312 (2004), pp. 69-85. http://geodesic.mathdoc.fr/item/ZNSL_2004_312_a8/