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The short history of L.Kantorovich's transport problem and his metric in theframework of his activity in mathmatics and economics during a long anddifficult period. We did not mention the recent impetuious developement ofapplication of the transport probelm to differential equations etc., andconcentrated on three applications not known to wide audience - in measure andergodic theory, and metric geometry and classification of mertric spaces withmeasures.  This is a detale version of the talk of author on the Conference devoted to  90-th annyversary of Leonid.V.Kantorovich which was at St.Petersbutrg EulerInternational Mathematical Institute in January 2004.

Kantorovich Metric: Initial History and Little-Known Applications