A Surjective Morphism from an object to itself. In Ergodic Theory, let be a Set, a Sigma Algebra on and a Probability Measure. A Map is called an endomorphism or Measure-Preserving Transformation if
An endomorphism is called Ergodic if it is true that Implies or 1, where .
See also Measurable Function, Measure-Preserving Transformation, Morphism, Sigma Algebra, Surjective