|
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
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.
Received: 24.01.2017 Revised: 15.02.2017
Citation:
A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333
Linking options:
https://www.mathnet.ru/eng/rm9763https://doi.org/10.1070/RM9763 https://www.mathnet.ru/eng/rm/v72/i2/p67
|
Statistics & downloads: |
Abstract page: | 907 | Russian version PDF: | 244 | English version PDF: | 31 | References: | 79 | First page: | 43 |
|