An ergodic IP polynomial Szemerédi theorem

An ergodic IP polynomial Szemerédi theorem

by Bergelson, V., (Vitaly)

Type Book
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Proves a polynomial multiple recurrence theorem for finitely, many commuting, measure-preserving transformations of a probability space, extending a polynomial Szemeredi theorem. Several applications to the structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which the authors also prove a multiparameter weakly mixing polynomial ergodic theorem. Techniques and apparatus employed include a polynomialization of an IP structure theory, an extension …

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Title Statements

  • Full title :An ergodic IP polynomial Szemerédi theorem / Vitaly Bergelson, Randall McCutcheon.

Summary

Proves a polynomial multiple recurrence theorem for finitely, many commuting, measure-preserving transformations of a probability space, extending a polynomial Szemeredi theorem. Several applications to the structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which the authors also prove a multiparameter weakly mixing polynomial ergodic theorem. Techniques and apparatus employed include a polynomialization of an IP structure theory, an extension of Hindman's theorem due to Milliken and Taylor, a polynomial version of the Hales-Jewett coloring theorem, and a theorem concerning limits of polynomially generated IP systems of unitary operators. Author information is not given. Annotation copyrighted by Book News, Inc., Portland, OR.

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Edition Statements

  • Publication Date:©2000.

Publication Statements

Notes

"July 2000, volume 146, number 695 (fourth of 5 numbers)."

The Physical Object

  • Description:1 online resource (viii, 106 pages)

Edition Identifiers

  • ISBN:9781470402860, 1470402866
  • oclc:ocn851086219
  • LC Classification:QA3.A57 no. 695 +
  • Dewey Decimal:510 s 515/.42

Subjects

Measure-preserving transformations Ramsey theory Théorie de Ramsey Transformations conservant la mesure

Writers

Bergelson, V., (Vitaly) McCutcheon, Randall

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