# Definition:Pi-System

## Theorem

Let $X$ be a set.

Let $\Pi \subseteq \map {\mathcal P} X$ be a collection of subsets of $X$.

We say that $\Pi$ is a $\pi$-system if and only if it is closed under finite intersection.

That is:

for all finite collections $A_1, A_2, \ldots, A_n$ of sets in $\Pi$ we have $\ds \bigcap_{i \mathop = 1}^n A_i \in \Pi$