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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 390, Pages 201–209 (Mi znsl4551)  
This article is cited in 12 scientific papers (total in 12 papers)

Correction of metrics

P. B. Zatitskiyab, F. V. Petrovb

a Saint-Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (192 kB) Citations (12)
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Abstract: We prove that a symmetric nonnegative function of two variables on a Lebesgue space that satisfies the triangle inequality for almost all triples of points is equivalent to some semimetric. Some other properties of metric triples (spaces with structures of a measure space and a metric space) are discussed.
Key words and phrases: Lebesgue space, semimetric.
Received: 01.10.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 181, Issue 6, Pages 867–870
DOI: https://doi.org/10.1007/s10958-012-0720-8
Bibliographic databases:
Document Type: Article
UDC: 517.518.115+517.987.1+515.124.4
Language: Russian
Citation: P. B. Zatitskiy, F. V. Petrov, “Correction of metrics”, Representation theory, dynamical systems, combinatorial methods. Part XX, Zap. Nauchn. Sem. POMI, 390, POMI, St. Petersburg, 2011, 201–209; J. Math. Sci. (N. Y.), 181:6 (2012), 867–870
Citation in format AMSBIB
\Bibitem{ZatPet11}
\by P.~B.~Zatitskiy, F.~V.~Petrov
\paper Correction of metrics
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XX
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 390
\pages 201--209
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4551}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 181
\issue 6
\pages 867--870
\crossref{https://doi.org/10.1007/s10958-012-0720-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84858745149}
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  • https://www.mathnet.ru/eng/znsl/v390/p201
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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