pi-system

Let $\mathrm{\Omega }$ be a set, and $𝒫(\mathrm{\Omega })$ be the power set of $\mathrm{\Omega }$. A $\pi$-system (or pi-system) on $\mathrm{\Omega }$ is a set $ℱ\subseteq 𝒫(\mathrm{\Omega })$ such that

$$A,B\in ℱ\Rightarrow A\cap B\in ℱ.$$ (1)

A $\pi$-system is closed under finite intersection.

Title	pi-system
Canonical name	Pisystem
Date of creation	2013-03-22 12:21:23
Last modified on	2013-03-22 12:21:23
Owner	drummond (72)
Last modified by	drummond (72)
Numerical id	4
Author	drummond (72)
Entry type	Definition
Classification	msc 03E20
Classification	msc 28A60
Related topic	DynkinSystem
Related topic	SigmaAlgebra
Related topic	DynkinsLemma