Definition:Trivial Factor of Measure-Preserving Dynamical System

Definition

Let $\struct {X, \BB, \mu, T}$ be a measure-preserving dynamical systems.

Let $\struct {Y, \CC, \nu, S}$ is called a factor of $\struct {X, \BB, \mu, T}$.

$\struct {Y, \CC, \nu, S}$ is a trivial factor if and only if $\struct {Y, \CC, \nu}$ is a singleton measure space, i.e.:

$\exists \set y \in \CC : \map \nu {\set y} = 1$

Sources

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