A D1109: Measurable set $E \in \mathcal{F}$ is

**stationary**in $M$ if and only if \begin{equation} T^{-1}(E) = E \end{equation}

Definition D2841

Stationary measurable set

Formulation 0

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}

A D1109: Measurable set $E \in \mathcal{F}$ is

Children

▶ | Ergodic measure |

▶ | Set of stationary measurable sets |

▶ | Stationary event |

Results

▶ | Complement of stationary measurable set is stationary |

▶ | Countable union of stationary measurable sets is stationary |

▶ | Empty set is a stationary measurable set |