Measure-preserving dynamical system

In mathematics,measure-preserving dynamical systeman objectstudy inabstract formulationergodic theory.

Itdefined asprobability space andmeasure-preserving transformation on it. In more detail, itsystem withfollowing structure:

isset,

is-algebra over ,

isprobability measure, so that , and

ismeasurable transformation which preservesmeasure , i. e. each measurable satisfies .

For example m could benormalised angle measure dθ/2π onunit circle,Trotation.