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This article is cited in 8 scientific papers (total in 8 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
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). |
DOI:
https://doi.org/10.4213/rm9763
 Full text:
PDF file (1196 kB)
 First page: PDF file
References:
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English version:
Russian Mathematical Surveys, 2017, 72:2, 257–333
Bibliographic databases:
    
UDC:
517.518
MSC: 05A05, 37A60, 37M99, 28A06, 60A10
Received: 24.01.2017
Revised: 15.02.2017
Citation:
A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Uspekhi Mat. Nauk, 72:2(434) (2017), 67–146; Russian Math. Surveys, 72:2 (2017), 257–333
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/umn9763https://doi.org/10.4213/rm9763 http://mi.mathnet.ru/eng/umn/v72/i2/p67
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