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}
▶ | Ergodic measure |
▶ | Set of stationary measurable sets |
▶ | Stationary event |
▶ | Complement of stationary measurable set is stationary |
▶ | Countable union of stationary measurable sets is stationary |
▶ | Empty set is a stationary measurable set |