An Ergodic IP Polynomial Szemeredi Theorem
Seiten
2000
American Mathematical Society (Verlag)
978-0-8218-2657-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-2657-7 (ISBN)
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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]. This book describes several applications to the fine structure of recurrence in ergodic theory.
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]).
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]).
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.
| Erscheint lt. Verlag | 1.8.2000 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 227 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-8218-2657-3 / 0821826573 |
| ISBN-13 | 978-0-8218-2657-7 / 9780821826577 |
| Zustand | Neuware |
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