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
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