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Zapiski Nauchnykh Seminarov 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
Full-text PDF (228 kB) Citations (2)
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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.
Received: 22.02.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 196, Issue 2, Pages 138–143
DOI: https://doi.org/10.1007/s10958-013-1645-6
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
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://mathscinet.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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  • https://www.mathnet.ru/eng/znsl/v411/p38
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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