An ergodic IP polynomial Szemerédi theorem
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Bibliographic Information
An ergodic IP polynomial Szemerédi theorem
（Memoirs of the American Mathematical Society, no. 695）
American Mathematical Society, 2000
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"July 2000, volume 146, number 695 (fourth of 5 numbers)"
References: p. 103-104
Description and Table of Contents
Description
We prove a polynomial multiple recurrence theorem for finitely many commuting measure preserving transformations of a probability space, extending a polynomial Szemeredi theorem appearing in [BL1]. The linear case is a consequence of an ergodic IP-Szemeredi theorem of Furstenberg and Katznelson ([FK2]). Several applications to the fine structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which we also prove a multiparameter weakly mixing polynomial ergodic theorem. The techniques and apparatus employed include a polynomialization of an IP structure theory developed in [FK2], an extension of Hindman's theorem due to Milliken and Taylor ([M], [T]), a polynomial version of the Hales-Jewett coloring theorem ([BL2]), and a theorem concerning limits of polynomially generated IP-systems of unitary operators ([BFM]).
Table of Contents
Introduction Formulation of main theorem Preliminaries Primitive extensions Relative polynomial mixing Completion of the proof Measure-theoretic applications Combinatorial applications For future investigation Appendix: Multiparameter weakly mixing PET References Index of notation Index.
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