Definition 13.2.1 ($\pi$-System). Let $X$ be a set and $\mathcal{P}\subset 2^{X}$, then $\mathcal{P}$ is a $\pi$-system if:
$\emptyset \in \mathcal{P}$.
For any $A, B \in \mathcal{P}$, $A \cap B \in \mathcal{P}$.
Definition 13.2.1 ($\pi$-System). Let $X$ be a set and $\mathcal{P}\subset 2^{X}$, then $\mathcal{P}$ is a $\pi$-system if:
$\emptyset \in \mathcal{P}$.
For any $A, B \in \mathcal{P}$, $A \cap B \in \mathcal{P}$.