Definition:Measure-Preserving Dynamical System

Definition

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

Let $T: X \to X$ be a measure-preserving transformation.

Then $\struct {X, \BB, \mu, T}$ is called to be a measure-preserving dynamical system.

Sources

• 2011: Manfred Einsiedler and Thomas Ward: Ergodic Theory: with a view towards Number Theory ... (previous) ... (next) $2.1$: Measure-Preserving Transformations