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arXiv · 1705.06619

The theory of filtrations of subalgebras, standardness and independence

Anatoly Vershik
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Abstract

The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $σ$-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. We discuss the possibility of obtaining a~classification of filtrations, their invariants, and various links to problems in algebra, dynamics, and combinatorics.

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Anatoly Vershik. 2017-05-18. The theory of filtrations of subalgebras, standardness and independence. https://doi.org/10.1070/rm9763

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