Abstract
In this chapter the basic objects studied in ergodic theory, measure-preserving transformations, are introduced. Some examples are given, and the relationship between various mixing properties is described. The mean and pointwise ergodic theorems are proved. An approach to the maximal ergodic theorem via a covering lemma is given, which will be extended in Chapter 8 to more general group actions.
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© 2011 Springer-Verlag London Limited
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Einsiedler, M., Ward, T. (2011). Ergodicity, Recurrence and Mixing. In: Ergodic Theory., vol 259. Springer, London. https://doi.org/10.1007/978-0-85729-021-2_2
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DOI: https://doi.org/10.1007/978-0-85729-021-2_2
Publisher Name: Springer, London
Print ISBN: 978-0-85729-020-5
Online ISBN: 978-0-85729-021-2
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