(i) | $f : X \to Y$ is a D201: Measurable map on $M$ |

**stationary**on $M$ if and only if \begin{equation} f \circ T = f \end{equation}

▾ 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

▾ 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

Formulation 0

Let $M = (X, \mathcal{F}, \mu, T)$ be a D2827: Measure-preserving system such that

Then $f$ is **stationary** on $M$ if and only if
\begin{equation}
f \circ T
= f
\end{equation}

(i) | $f : X \to Y$ is a D201: Measurable map on $M$ |