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ArticleOriginal scientific text

Title

On measure theoretical analogues of the Takesaki structure theorem for type III factors

Authors 1, 2

Affiliations

  1. Department of Mechanics and Mathematics, Kharkov National University, Freedom square 4, Kharkov, 61077, Ukraine
  2. Graduate School of Mathematics, Kyushu University, Ropponmatsu Chuo-ku, Fukuoka, 810-8560, Japan

Abstract

The orbit equivalence of type III0 ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type III0 cocycles with values in Abelian groups.

Bibliography

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Colloquium Mathematicum
2000/84/85/2
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Pages:
485-493
Main language of publication
English
Received
1999-09-22
Accepted
2000-03-15
Published
2000
Exact and natural sciences