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ArticleOriginal scientific text

Title

Relatively perfect σ-algebras for flows

Authors 1, 2

Affiliations

  1. Centre National, De la Recherche Scientifique, Laboratoire de Mathématiques Discrètes, UPR 9016-163, Avenue de Luminy-Case 930,13288 Marseille Cedex 9, France
  2. Wydział Matematyki i Informatyki, Uniwersytet Mikołaja Kopernika, ul. Chopina 12/18, 87-100 Toruń, Poland

Abstract

We show that for every ergodic flow, given any factor σ-algebra ℱ, there exists a σ-algebra which is relatively perfect with respect to ℱ. Using this result and Ornstein's isomorphism theorem for flows, we give a functorial definition of the entropy of flows.

Keywords

ENG
entropy, flow, principal factor, relatively excellent σ-algebra, relatively perfect σ-algebra

Bibliography

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Studia Mathematica
1995/114/1
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Pages:
71-85
Main language of publication
English
Received
1994-03-10
Accepted
1994-12-30
Published
1995
Exact and natural sciences