Let $P = (\Omega, \mathcal{F}, \mathbb{P}, T)$ be a D2839: Probability-preserving system such that
Let $n \in \mathbb{N}$ be a D996: Natural number.
(i) | $E \in \mathcal{F}$ is an D1716: Event in $P$ |
(ii) | \begin{equation} \mathbb{P} \left( E \triangle T^{-1} E \right) = 0 \end{equation} |
Then
\begin{equation}
\mathbb{P} \left( E \triangle T^{-n} E \right)
= 0
\end{equation}