Definition:Ergodic Measure-Preserving Transformation/Definition 3

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 $A \in \BB$:
 * $\map\mu {A}>0 \implies \map \mu {\bigcup _{n=1}^\infty T^{-1} \sqbrk A}=1$