RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zap. Nauchn. Sem. 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

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.

Full text: PDF file (293 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2013, 190:3, 427–437

Bibliographic databases:

UDC: 517.987
Received: 10.10.2012

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://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880605064}


Linking options:
  • http://mi.mathnet.ru/eng/znsl5247
  • http://mi.mathnet.ru/eng/znsl/v403/p35

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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
    3. J. Math. Sci. (N. Y.), 200:6 (2014), 677–681  mathnet  crossref
    4. 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
    5. J. Math. Sci. (N. Y.), 219:5 (2016), 683–699  mathnet  crossref  mathscinet
    6. Vershik A.M., “Asymptotic theory of path spaces of graded graphs and its applications”, Jap. J. Math., 11:2 (2016), 151–218  crossref  mathscinet  zmath  isi  scopus
    7. 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
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:174
    Full text:52
    References:38

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019