Definition:Weakly 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 weakly mixing :
 * $\ds \forall A, B \in \BB : \lim_{N \mathop\to \infty} \frac 1 N \sum _{n \mathop = n}^{N-1} \size {\map \mu {A \cap T^{-n} \sqbrk B} - \map \mu A \map \mu B} = 0$

Also see

 * Definition:Ergodic Measure-Preserving Transformation
 * Definition:Strongly Mixing Measure-Preserving Transformation