Definition:Measure-Preserving Transformation

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

Let $T: X \to X$ be a measurable mapping.

$T$ is said to be a measure-preserving transformation if $\mu$ is invariant under $T$.

Also known as
More explicitly, it is also called $\mu$-preserving transformation.

Also see

 * Definition:Invariant Measure
 * Definition:Measure-Preserving Mapping
 * Definition:Ergodic Measure-Preserving Transformation