Definition:Weakly Mixing Measure-Preserving Transformation/Definition 2
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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 if and only if:
- $T \times T$ is ergodic with respect to $\mu \times \mu$
where $\mu \times \mu$ denotes the product measure on $\struct {X \times X, \BB \otimes \BB}$.
Sources
- 2011: Manfred Einsiedler and Thomas Ward: Ergodic Theory: with a view towards Number Theory $2.7$: Strong-Mixing and Weak-Mixing