ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Subset
▼ Power set
▼ Hyperpower set sequence
▼ Hyperpower set
▼ Hypersubset
▼ Subset algebra
▼ Subset structure
▼ Measurable space
▼ Measure space
▼ Measure-preserving endomorphism
▼ Measure-preserving system
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}
Children
▶ D3059: Ergodic measure
▶ D2842: Set of stationary measurable sets
▶ D4489: Stationary event
Results
▶ 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