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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 403, Pages 35–57 (Mi znsl5247)  
This article is cited in 6 scientific papers (total in 7 papers)

On classification of measurable functions of several variables

A. M. Vershik

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (293 kB) Citations (7)
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Abstract: We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations, describe a new complete system of its invariants (the system of joint distributions), and relate these notions to matrix distributions, i.e., another invariant of measurable functions, which was found earlier and is a random matrix.
Key words and phrases: classification of functions, matrix distribution, canonical form, joint distributions.
Received: 10.10.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 190, Issue 3, Pages 427–437
DOI: https://doi.org/10.1007/s10958-013-1258-0
Bibliographic databases:
Document Type: Article
UDC: 517.987
Language: Russian
Citation: A. M. Vershik, “On classification of measurable functions of several variables”, Representation theory, dynamical systems, combinatorial methods. Part XXI, Zap. Nauchn. Sem. POMI, 403, POMI, St. Petersburg, 2012, 35–57; J. Math. Sci. (N. Y.), 190:3 (2013), 427–437
Citation in format AMSBIB
\Bibitem{Ver12}
\by A.~M.~Vershik
\paper On classification of measurable functions of several variables
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXI
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 403
\pages 35--57
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5247}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3029579}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 190
\issue 3
\pages 427--437
\crossref{https://doi.org/10.1007/s10958-013-1258-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880605064}
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  • https://www.mathnet.ru/eng/znsl/v403/p35
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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