Abstract
When a system is not ergodic, it is possible to decompose the underlying space into several pieces, so that the transformation is ergodic on each of these pieces. We call this a partition into ergodic components. The number of components may be uncountable, but the resulting partition still satisfies a certain regularity property: it is possible to approximate it with partitions having finitely many pieces.
I was very concretely minded (…). Yet I felt a little bit that I ought to do these abstract things, and Steinhaus, whom I met a little later, said, “You shouldn’t; you must earn the right to generalize.” M. Kac (1914–1984)
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Coudène, Y. (2016). Ergodic Decomposition. In: Ergodic Theory and Dynamical Systems. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-7287-1_14
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DOI: https://doi.org/10.1007/978-1-4471-7287-1_14
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