▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Subset
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▾ Hyperpower set sequence
▾ Hyperpower set
▾ Hypersubset
▾ Subset algebra
▾ Subset structure
▾ Measurable space
▾ Measure space
▾ Measure-preserving endomorphism
▾ Measure-preserving system
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}
Child definitions
» D3059: Ergodic measure
» D2842: Set of stationary measurable sets
» D4489: Stationary event
Results
» R4437: Complement of stationary measurable set is stationary
» R4466: Whole space is a stationary measurable set
» R4467: Empty set is a stationary measurable set
» R4469: Countable union of stationary measurable sets is stationary