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}