ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation 0
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 $P$
(ii) \begin{equation} \mathbb{P} \left( E \triangle T^{-1} E \right) = 0 \end{equation}
Let $n \in \mathbb{N}$ be a D996: Natural number.
Then \begin{equation} \mathbb{P} \left( E \triangle T^{-n} E \right) = 0 \end{equation}