Furstenberg's Proof of Szemerédi's Theorem

Manfred Einsiedler () and Thomas Ward ()
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Manfred Einsiedler: ETH Zurich, Departement Mathematik
Thomas Ward: University of East Anglia, School of Mathematics

Chapter Chapter 7 in Ergodic Theory, 2011, pp 171-230 from Springer

Abstract: 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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-85729-021-2_7

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DOI: 10.1007/978-0-85729-021-2_7

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