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

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

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.

Full text: PDF file (271 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519
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} 

• http://mi.mathnet.ru/eng/znsl6229
• http://mi.mathnet.ru/eng/znsl/v441/p119

 SHARE:

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
2. A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333
•  Number of views: This page: 83 Full text: 15 References: 23