Measure-preserving dynamical system
In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of ergodic theory.
It is defined as a probability space and a measure-preserving transformation on it. In more detail, it is system  with the following structure:
 is a set,
 is a  -algebra over ,
 is a probability measure, so that  , and
 is a measurable transformation which preserves the measure  , i. e. each measurable  satisfies  .
For example m could be the normalised angle measure dθ/2π on the unit circle, and T a rotation.
Referenced By
List of dynamical system and differential equation topics | List of dynamical system topics
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