Definition:Measure-Preserving Dynamical System
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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