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} \left\{ X \in \bigcup_{n \in \mathbb{N}} B_n \right\} = \bigcup_{n \in \mathbb{N}} \{ X \in B_n \} \end{equation}

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} \left\{ \omega \in \Omega : X(\omega) \in \bigcup_{n \in \mathbb{N}} B_n \right\} = \bigcup_{n \in \mathbb{N}} \{ \omega \in \Omega : X(\omega) \in B_n \} \end{equation}