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

- 1. is Surjective,
- 2. is Measurable,
- 3. for all .

An endomorphism is called Ergodic if it is true that Implies or 1, where .

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1999-05-25