# pi-system

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

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

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

Title pi-system Pisystem 2013-03-22 12:21:23 2013-03-22 12:21:23 drummond (72) drummond (72) 4 drummond (72) Definition msc 03E20 msc 28A60 DynkinSystem SigmaAlgebra DynkinsLemma