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
▼ Finitary measure-preserving endosystem
▼ Strongly mixing measure-preserving system
Definition D5573
Strongly mixing probability-preserving system
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P}, T)$ be a D2839: Probability-preserving system.
Then $P$ is a strongly mixing probability-preserving system if and only if \begin{equation} \forall \, E, F \in \mathcal{F} : \lim_{n \to \infty} \mathbb{P}(E \cap T^{-n} F) = \mathbb{P}(E) \mathbb{P}(F) \end{equation}