Definition:Strongly Mixing Measure-Preserving Transformation

Definition

Let $\struct {X, \BB, \mu}$ be a probability space.

Let $T: X \to X$ be a measure-preserving transformation.

$T$ is said to be strongly mixing if and only if:

$\ds \forall A, B \in \BB : \lim_{n \mathop\to \infty} \map \mu {A \cap T^{-n} \sqbrk B} = \map \mu A \map \mu B$

Also see

• Definition:Ergodic Measure-Preserving Transformation
• Definition:Weakly Mixing Measure-Preserving Transformation

Sources

• 2011: Manfred Einsiedler and Thomas Ward: Ergodic Theory: with a view towards Number Theory: Chapter $2$: Ergodicity, Recurrence and Mixing