Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) | $\mathcal{G}_0, \mathcal{G}_1, \mathcal{G}_2, \ldots \subseteq \mathcal{F}$ are each a D470: Subsigma-algebra of $\mathcal{F}$ on $\Omega$ |
(i) | $\mathcal{G}_0, \mathcal{G}_1, \mathcal{G}_2, \ldots$ is an D471: Independent collection of sigma-algebras on $P$ |
(iii) | $\mathcal{G}_{\infty}$ is the D3889: Tail sigma-algebra on $\Omega$ with respect to $\mathcal{G}_0, \mathcal{G}_1, \mathcal{G}_2, \ldots$ |
(iv) | $E \in \mathcal{G}_{\infty}$ is an D1716: Event in $(\Omega, \mathcal{F}_{\infty}, \mathbb{P})$ |
Then
\begin{equation}
\mathbb{P}(E) \in \{ 0, 1 \}
\end{equation}