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 D4489
Stationary event
Formulation 0
Let $S = (\Omega, \mathcal{F}, \mathbb{P}, T)$ be a D2839: Probability-preserving system.
An D1716: Event $E \in \mathcal{F}$ is stationary in $S$ if and only if \begin{equation} T^{-1}(E) = E \end{equation}
Formulation 1
Let $S = (\Omega, \mathcal{F}, \mathbb{P}, T)$ be a D2839: Probability-preserving system.
An D1716: Event $E \in \mathcal{F}$ in $(\Omega, \mathcal{F}, \mathbb{P})$ is stationary with respect to $T$ if and only if \begin{equation} T^{-1} E = E \end{equation}