Let $P = (\Omega, \mathcal{F}, \mathbb{P}, T)$ be a D2839: Probability-preserving system such that

(i)	$E \in \mathcal{F}$ is an D1716: Event in $P$

Then \begin{equation} \forall \, n \in \mathbb{N} : \mathbb{P}(T^{-n} E) = \mathbb{P}(E) \end{equation}

Let $P = (\Omega, \mathcal{F}, \mathbb{P}, T)$ be a D2839: Probability-preserving system such that

(i)	$E \in \mathcal{F}$ is an D1716: Event in $P$

Then \begin{equation} \mathbb{P}(E) = \mathbb{P}(T^{-1} E) = \mathbb{P}(T^{-2} E) = \mathbb{P}(T^{-3} E) = \cdots \end{equation}