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Zap. Nauchn. Sem. POMI, 2011, Volume 390, Pages 201–209 (Mi znsl4551)  

This article is cited in 9 scientific papers (total in 9 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

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.

Full text: PDF file (192 kB)
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English version:
Journal of Mathematical Sciences (New York), 2012, 181:6, 867–870

Document Type: Article
UDC: 517.518.115+517.987.1+515.124.4
Received: 01.10.2011

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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84858745149}


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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. A. M. Vershik, P. B. Zatitskii, F. V. Petrov, “Virtual Continuity of Measurable Functions of Several Variables and Embedding Theorems”, Funct. Anal. Appl., 47:3 (2013), 165–173  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. M. Vershik, P. B. Zatitskiy, F. V. Petrov, “Virtual continuity of measurable functions and its applications”, Russian Math. Surveys, 69:6 (2014), 1031–1063  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. P. B. Zatitskii, “On a Scaling Entropy Sequence of a Dynamical System”, Funct. Anal. Appl., 48:4 (2014), 291–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. P. B. Zatitskiy, “Scaling entropy sequence: invariance and examples”, J. Math. Sci. (N. Y.), 209:6 (2015), 890–909  mathnet  crossref
    5. P. B. Zatitskiy, “On the possible growth rate of a scaling entropy sequence”, J. Math. Sci. (N. Y.), 215:6 (2016), 715–733  mathnet  crossref  mathscinet
    6. P. B. Zatitskiy, F. V. Petrov, “On the subadditivity of a scaling entropy sequence”, J. Math. Sci. (N. Y.), 215:6 (2016), 734–737  mathnet  crossref  mathscinet
    7. F. Petrov, “Correcting continuous hypergraphs”, St. Petersburg Math. J., 28:6 (2017), 783–787  mathnet  crossref  isi  elib
    8. A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. A. M. Vershik, P. B. Zatitskii, “Universal adic approximation, invariant measures and scaled entropy”, Izv. Math., 81:4 (2017), 734–770  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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