Kantorovich metric:initial history and little-known applications

TL;DR

This paper explores the historical development of the Kantorovich metric and highlights lesser-known applications in measure theory, ergodic theory, metric geometry, and classification of metric spaces with measures.

Contribution

It provides a detailed historical overview and uncovers novel applications of the Kantorovich metric in various mathematical fields beyond its traditional uses.

Findings

Application in measure and ergodic theory

Use in metric geometry and classification of metric spaces with measures

Historical analysis of Kantorovich's transport problem and metric

Abstract

The short history of L.Kantorovich's transport problem and his metric in the framework of his activity in mathmatics and economics during a long and difficult period. We did not mention the recent impetuious developement of application of the transport probelm to differential equations etc., and concentrated on three applications not known to wide audience - in measure and ergodic theory, and metric geometry and classification of mertric spaces with measures. 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 Euler International Mathematical Institute in January 2004.