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Funktsional'nyi Analiz i ego Prilozheniya, 2023, Volume 57, Issue 4, Pages 46–59
DOI: https://doi.org/10.4213/faa4166 (Mi faa4166) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Classification of measurable functions of several variables and matrix distributions

A. M. Vershikabc

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
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DOI: https://doi.org/10.4213/faa4166
Abstract: We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, this is an invariant of this function with respect to a certain group of transformations of variables; on the other hand, this is a special probability measure in the space of matrices (tensors) that is invariant under actions of natural infinite permutation groups. The intricate interplay of both interpretations of matrix (tensor) distributions makes them an important subject of modern functional analysis. We formulate and prove a theorem that, under certain conditions on a measurable function of two variables, its matrix distribution is a complete invariant.
Keywords: classification of functions, matrix distribution, metric triples, pointwise ergodic theorem.
Funding agency Grant number
Russian Science Foundation 21-11-00152
Received: 15.10.2023
Revised: 15.10.2023
Accepted: 20.10.2023
English version:
Functional Analysis and Its Applications, 2023, Volume 57, Issue 4, Pages 303–313
DOI: https://doi.org/10.1134/S0016266323040044
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. M. Vershik, “Classification of measurable functions of several variables and matrix distributions”, Funktsional. Anal. i Prilozhen., 57:4 (2023), 46–59; Funct. Anal. Appl., 57:4 (2023), 303–313
Citation in format AMSBIB
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\paper Classification of measurable functions of several variables and matrix distributions
\jour Funktsional. Anal. i Prilozhen.
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\issue 4
\pages 46--59
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\jour Funct. Anal. Appl.
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\pages 303--313
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  • https://doi.org/10.4213/faa4166
  • https://www.mathnet.ru/eng/faa/v57/i4/p46
    • This publication is cited in the following 1 articles:
    1. A. M. Vershik, G. A. Veprev, P. B. Zatitskii, “Dynamics of metrics in measure spaces and scaling entropy”, Russian Math. Surveys, 78:3 (2023), 443–499  mathnet  mathnet  crossref  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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