# The theory of filtrations of subalgebras, standardness and independence

## TL;DR

This survey explores the combinatorial and metric theory of filtrations, focusing on standardness as a generalization of independence, and discusses classification, invariants, and connections to algebra, dynamics, and combinatorics.

## Contribution

It provides a comprehensive overview of the theory of filtrations, emphasizing the concept of standardness and its role in classification and invariants.

## Key findings

- Standardness generalizes independence in filtrations.
- Potential classification schemes for filtrations are discussed.
- Connections to algebra, dynamics, and combinatorics are explored.

## Abstract

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