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}

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}

Then $P$ is a