ThmDex – An index of mathematical definitions, results, and conjectures.
F10025
Formulation 1
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 $P$
(ii) \begin{equation} \mathbb{P}(E_0) = 1 \end{equation}
Then \begin{equation} \mathbb{P} \left( E_n \text{ happens for any } n \in \mathbb{N} \right) = 1 \end{equation}