On the Equality of Values in the Monge and Kantorovich Problems


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This paper is concerned with the study of conditions under which the Monge and Kantorovich problems with a continuous cost function on a product of two completely regular spaces and two given atomless Radon measures-projections on these spaces have equal values of the corresponding infima.

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V. Bogachev

Lomonosov Moscow State University; National Research University Higher School of Economics; Orthodox St.Tikhon Humanitarian University

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Email: vibogach@mail.ru
俄罗斯联邦, Moscow

A. Kalinin

Lomonosov Moscow State University

Email: vibogach@mail.ru
俄罗斯联邦, Moscow

S. Popova

Lomonosov Moscow State University

Email: vibogach@mail.ru
俄罗斯联邦, Moscow

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