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
▼ Stationary measurable set
Definition D2842
Set of stationary measurable sets
Formulation 0
Let $M = (X, \mathcal{F}, \mu, T)$ be a D2827: Measure-preserving system.
The set of stationary measurable sets in $M$ is the D11: Set \begin{equation} \left\{ E \in \mathcal{F} : T^{-1} E = E \right\} \end{equation}
Children
▶ D2840: Ergodic measure-preserving system
▶ D4490: Set of stationary events
Results
▶ R4468: Set of stationary measurable sets is a sigma-algebra