---
tag: V5M2CKB591
kind: concept
name: Dynkin system
msc: [28A05, 60A10]
sources:
  - url: https://en.wikipedia.org/wiki/Dynkin_system
same_as:
  wikidata: Q1935689
  wikipedia: Dynkin system
---

## Summary

A Dynkin system, or λ-system, on a set $X$ is a family of subsets that contains $X$.
It is closed under complements and under countable unions of disjoint members.
It is weaker than a σ-algebra, because it need not be closed under intersections.
Dynkin systems appear in the π-λ theorem, the standard tool to prove that two measures are equal.

## Explanations

### L1 human

A Dynkin system is the kind of family one gets when one collects all sets on which two probability measures agree.
Such a family is stable under complements and disjoint countable unions, but in general not under intersections.
A small example: on $\set{1, 2, 3, 4}$, the subsets with an even number of elements form a Dynkin system.
It is not a σ-algebra, since $\set{1, 2} \cap \set{2, 3} = \set{2}$ has one element.