Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$X : \Omega \to \Xi$ is a D202: Random variable on $P$
(ii)	$\{ X \in B_0 \}, \{ X \in B_1 \}, \{ X \in B_2 \}, \ldots \in \mathcal{F}$ are each an D1716: Event in $P$

Then \begin{equation} \mathbb{P} \left( X \in \bigcap_{n \in \mathbb{N}} B_n \right) = \mathbb{P} \left( \bigcap_{n \in \mathbb{N}} \{ X \in B_n \} \right) \end{equation}