Ergodic decomposition |
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| Affiliation: | 1. Dept. of Mathematics, University of Houston, Houston, TX 77204, United States of America;2. Dept. of Mathematics, Ruhr University Bochum, 44780 Bochum, Germany;3. IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil;1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, 221116, PR China;2. Department of Mathematics, Shantou University, Shantou 515063, PR China |
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| Abstract: | Ergodic systems, being indecomposable are important part of the study of dynamical systems but if a system is not ergodic, it is natural to ask the following question: Is it possible to split it into ergodic systems in such a way that the study of the former reduces to the study of latter ones? Also, it will be interesting to see if the latter ones inherit some properties of the former one. This document answers this question for measurable maps defined on complete separable metric spaces with Borel probability measure, using the Rokhlin Disintegration Theorem. |
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