Definition:Ergodic Measure-Preserving Transformation/Definition 4

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 ergodic if for any $A,B \in \BB$:
 * $\map\mu A \map\mu B >0 \implies \exists n\geqslant 1:\,\map\mu {T^{-n}\sqbrk A\cap B}>0$