Let $M = (X, \mathcal{F}, \mu, T)$ be a D2827: Measure-preserving system.
A D1109: Measurable set $E \in \mathcal{F}$ is stationary in $M$ if and only if
\begin{equation}
T^{-1}(E) = E
\end{equation}
▶ | D3059: Ergodic measure |
▶ | D2842: Set of stationary measurable sets |
▶ | D4489: Stationary event |
▶ | R4437: Complement of stationary measurable set is stationary |
▶ | R4469: Countable union of stationary measurable sets is stationary |
▶ | R4467: Empty set is a stationary measurable set |