**probability-preserving system**if and only if $T$ is a D3120: Probability-preserving endomorphism on $S$.

▾ 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

▾ 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

Formulation 0

A D3116: Probabilistic endosystem $S = (\Omega, \mathcal{F}, \mathbb{P}, T)$ is **probability-preserving system** if and only if $T$ is a D3120: Probability-preserving endomorphism on $S$.

Also known as

Probability-preserving dynamical system

Child definitions

Results