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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 507, Pages 26–28
DOI: https://doi.org/10.31857/S2686954322600380 (Mi danma313) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

On Kantorovich problems with a parameter

V. I. Bogachevabc, S. N. Popovabd

a Lomonosov Moscow State University, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
c Saint-Tikhon’s Orthodox University, Moscow, Russia
d Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow, Russia
Citations (2)
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DOI: https://doi.org/10.31857/S2686954322600380
Abstract: In this note, we study the Kantorovich problem of optimal transportation of measures on metric spaces in the case where the cost function and marginal distributions depend on a parameter from a metric space. It is shown that the Hausdorff distance between the sets of probability measures with given marginals can be estimated by the distances between the marginals. As a corollary, it is proved that the cost of optimal transportation is continuous with respect to the parameter if the cost function and marginal distributions are continuous in this parameter.
Keywords: Kantorovich problem, Kantorovich metric, optimal plan, Hausdorff distance, continuity with respect to a parameter.
Funding agency Grant number
Russian Science Foundation 22-11-00015
This research is supported by the Russian Science Foundation, grant no. 22-11-00015.
Presented: V. V. Kozlov
Received: 01.06.2022
Revised: 30.10.2022
Accepted: 17.11.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 3, Pages 426–428
DOI: https://doi.org/10.1134/S1064562422700107
Bibliographic databases:
Document Type: Article
UDC: 517.987
Language: Russian
Citation: V. I. Bogachev, S. N. Popova, “On Kantorovich problems with a parameter”, Dokl. RAN. Math. Inf. Proc. Upr., 507 (2022), 26–28; Dokl. Math., 106:3 (2022), 426–428
Citation in format AMSBIB
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\paper On Kantorovich problems with a parameter
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\pages 26--28
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\crossref{https://doi.org/10.31857/S2686954322600380}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563841}
\elib{https://elibrary.ru/item.asp?id=49991279}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 3
\pages 426--428
\crossref{https://doi.org/10.1134/S1064562422700107}
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    • This publication is cited in the following 2 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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