On the Kantorovich problems with a parameter

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Abstract

We study measurable dependence of measures on a parameter in the Kantorovich optimal transportation problem with a parameter. Broad sufficient conditions are obtained for the existence of proper conditional measures measurably depending on a parameter in the case of parametric families of measures and mappings.

About the authors

V. I. Bogachev

Lomonosov Moscow State University; Higher School of Economics

Author for correspondence.
Email: vibogach@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991; 20, Myasnitskaya str., Moscow, 101000

I. I. Malofeev

Lomonosov Moscow State University; St. Tikhons Orthodox University

Email: vibogach@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991; 23/5a, Novokuznetskaya street, Moscow, 115184

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