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Zap. Nauchn. Sem. POMI, 2015, Volume 441, Pages 119–143 (Mi znsl6229)  

This article is cited in 2 scientific papers (total in 2 papers)

On the classification problem of measurable functions in several variables and on matrix distributions

A. M. Vershikab, U. Haböckc

a Steklov Inst. of Mathematics, St. Petersburg, Fontanka 27, St. Petersburg, 191023, Russia
b Math. Dept of St. Petersburg State University, Russia
c Cometence Centre for IT-Security, Fachhochschule Campus Wien, Favoritenstrasse 226, A-1100 Wien, Austria

Abstract: We resume the results from [12] on the classification of measurable functions in several variables, with some minor corrections of purely technical nature. We give a partial solution of he characterization problem of so-called matrix distributions, which are the metric invariants of measurable functions introduced in [12]. Matrix distibutions considered as $§_\mathbb N\times§_\mathbb N$-invariant, ergodic measures on the space of matrices – this fact connects our problem with Aldous' and Hoover's theorem [2,6].

Key words and phrases: classification of measurable functions, matrix distributions, pure functions, simple measures.

Funding Agency Grant Number
Russian Science Foundation 14-11-00581
The first author supported by the Russian Science Foundation grant # 14-11-00581.


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English version:
Journal of Mathematical Sciences (New York), 2016, 219:5, 683–699

Bibliographic databases:

UDC: 519
Received: 19.09.2015
Language:

Citation: A. M. Vershik, U. Haböck, “On the classification problem of measurable functions in several variables and on matrix distributions”, Probability and statistics. Part 22, Zap. Nauchn. Sem. POMI, 441, POMI, St. Petersburg, 2015, 119–143; J. Math. Sci. (N. Y.), 219:5 (2016), 683–699

Citation in format AMSBIB
\Bibitem{VerHab15}
\by A.~M.~Vershik, U.~Hab\"ock
\paper On the classification problem of measurable functions in several variables and on matrix distributions
\inbook Probability and statistics. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 441
\pages 119--143
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6229}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3504501}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 219
\issue 5
\pages 683--699
\crossref{https://doi.org/10.1007/s10958-016-3138-x}


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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. 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
    2. 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
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