Definition:Measure-Preserving Transformation
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Definition
Let $\struct {X, \BB, \mu}$ be a measure space.
Let $T: X \to X$ be a measurable mapping.
$T$ is called a measure-preserving transformation if and only if $\mu$ is invariant under $T$.
Also known as
More explicitly, $T$ is also called a $\mu$-preserving transformation.
Also see
- Definition:Invariant Measure
- Definition:Measure-Preserving Mapping
- Definition:Ergodic Measure-Preserving Transformation
- Definition: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