---
tag: 0B5BA4FRWS
kind: concept
name: Independent sigma-algebras
aliases: [independence-of-sigma-algebras]
msc: [60A05]
sources:
  - url: https://en.wikipedia.org/wiki/Independence_(probability_theory)
    locator: Independent σ-algebras
---

## Summary

A family of sub-σ-algebras of a probability space is independent when events chosen from different members of the family are always mutually independent.
It is the most general form of independence, and the independence of events and of random variables are special cases. The node [[independent sigma-algebras|09T8ZHST1V]] gives the precise definition.