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Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemerédi's theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal distal factor of a separable measure-preserving system can extend arbitrarily far into the countable ordinals. Here we show that the Furstenberg-Katznelson proof does not require the full strength of the maximal distal factor, in the sense that the proof only depends on a combinatorial weakening of its properties. We show that this combinatorially weaker property obtains fairly low in the transfinite construction, namely, by the $ω^{ω^{ω}}$th level.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
243-268
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Department of Philosophy, and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
autor
- Department of Mathematics, University of California, Los Angeles, CA 90095-1555, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm210-3-2