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Russian Mathematical Surveys, 2017, Volume 72, Issue 2, Pages 257–333
DOI: https://doi.org/10.1070/RM9763
(Mi rm9763)
 

This article is cited in 18 scientific papers (total in 18 papers)

The theory of filtrations of subalgebras, standardness, and independence

A. M. Vershikabc

a St. Petersburg Department of the Steklov Mathematical Institute
b St. Petersburg State University
c Institute for Information Transmission Problems
References:
Abstract: This survey is devoted to the combinatorial and metric theory of filtrations: decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of standardness, plays the role of a generalization of the notion of the independence of a sequence of random variables. Questions are discussed on the possibility of classifying filtrations, on their invariants, and on various connections with problems in algebra, dynamics, and combinatorics.
Bibliography: 101 titles.
Keywords: filtrations, $\sigma$-algebras, independence, standardness, graded graphs, central measures.
Funding agency Grant number
Russian Science Foundation 14-11-00581
Partially supported by the Russian Science Foundation (grant no. 14-11-00581).
Received: 24.01.2017
Revised: 15.02.2017
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: English
Original paper language: Russian
Citation: A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333
Citation in format AMSBIB
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\by A.~M.~Vershik
\paper The theory of filtrations of subalgebras, standardness, and independence
\jour Russian Math. Surveys
\yr 2017
\vol 72
\issue 2
\pages 257--333
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Linking options:
  • https://www.mathnet.ru/eng/rm9763
  • https://doi.org/10.1070/RM9763
  • https://www.mathnet.ru/eng/rm/v72/i2/p67
  • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:907
    Russian version PDF:244
    English version PDF:31
    References:79
    First page:43
     
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