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Zap. Nauchn. Sem. POMI, 2013, Volume 411, Pages 38–48 (Mi znsl5630)  

This article is cited in 1 scientific paper (total in 2 paper)

Two ways to define compatible metrics on the simplex of measures

A. M. Vershik

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We introduce two general methods of lifting a metric on a space to the simplex of probability measures on the metric space. The first one is the method of transportation plans, or the coupling method; the second one is the method of considering norms dual to the restrictions of the Lipschitz norm to subspaces. The intersection of these two classes of metrics consists of the Kantorovich metric.

Key words and phrases: Kantoroivch metric, admissible metrics, translational invariance, transportation problems.

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English version:
Journal of Mathematical Sciences (New York), 2014, 196:2, 138–143

Bibliographic databases:

UDC: 517.98
Received: 22.02.2013

Citation: A. M. Vershik, “Two ways to define compatible metrics on the simplex of measures”, Representation theory, dynamical systems, combinatorial methods. Part XXII, Zap. Nauchn. Sem. POMI, 411, POMI, St. Petersburg, 2013, 38–48; J. Math. Sci. (N. Y.), 196:2 (2014), 138–143

Citation in format AMSBIB
\Bibitem{Ver13}
\by A.~M.~Vershik
\paper Two ways to define compatible metrics on the simplex of measures
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXII
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 411
\pages 38--48
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5630}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3048267}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 196
\issue 2
\pages 138--143
\crossref{https://doi.org/10.1007/s10958-013-1645-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84897076572}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Vershik A.M., “Long History of the Monge-Kantorovich Transportation Problem”, Math. Intell., 35:4 (2013), 1–9  crossref  mathscinet  zmath  isi  scopus
    2. V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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