The theory of filtrations of subalgebras, standardness, and independence

A. M. Vershik

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 72 (2017) no. 2, pp. 257-333

Résumé

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.

Détail

Keywords: $\sigma$-algebras, independence, standardness, graded graphs, central measures.
Mots-clés : filtrations

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