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ArticleOriginal scientific text

Title

Simple systems are disjoint from Gaussian systems

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
  2. Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

We prove the theorem promised in the title. Gaussians can be distinguished from simple maps by their property of divisibility. Roughly speaking, a system is divisible if it has a rich supply of direct product splittings. Gaussians are divisible and weakly mixing simple maps have no splittings at all so they cannot be isomorphic. The proof that they are disjoint consists of an elaboration of this idea, which involves, among other things, the notion of virtual divisibility, which is, more or less, divisibility up to distal extensions. The theory of Kronecker Gaussians also plays a crucial role.

Bibliography

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Studia Mathematica
1999/133/3
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Pages:
249-256
Main language of publication
English
Received
1997-09-08
Accepted
1998-09-04
Published
1999
Exact and natural sciences