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.