Abstract
Furstenberg’s ergodic approach to Szemerédi’s Theorem is one of the highlights of this volume. We use the measure-theoretic machinery developed in Chapters 5 and 6 to give a careful proof of Furstenberg’s multiple recurrence theorem. To help motivate the proof we consider several special cases first, including the case of weak-mixing and discrete spectrum systems, and Roth’s theorem. A simple proof of van der Waerden’s theorem is given, and we show how this may be used to simplify one step in Furstenberg’s proof.
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© 2011 Springer-Verlag London Limited
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Einsiedler, M., Ward, T. (2011). Furstenberg's Proof of Szemerédi's Theorem. In: Ergodic Theory., vol 259. Springer, London. https://doi.org/10.1007/978-0-85729-021-2_7
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DOI: https://doi.org/10.1007/978-0-85729-021-2_7
Publisher Name: Springer, London
Print ISBN: 978-0-85729-020-5
Online ISBN: 978-0-85729-021-2
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