▾ 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
▾ Almost stationary measurable map
Stationary measurable map
Formulation 0
Let $M = (X, \mathcal{F}, \mu, T)$ be a D2827: Measure-preserving system such that
(i) $f : X \to Y$ is a D201: Measurable map on $M$
Then $f$ is stationary on $M$ if and only if \begin{equation} f \circ T = f \end{equation}