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

(i) | $E_0, E_1, E_2, \ldots \in \mathcal{F}$ are each an D1716: Event in $P$ |

Then
\begin{equation}
\mathbb{P} \left( \bigcup_{n \in \mathbb{N}} E_n \right)
\leq \sum_{n \in \mathbb{N}} \mathbb{P}(E_n)
\end{equation}