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

Volume 84 / 2000

Alexandre Danilenko, Toshihiro Hamachi Colloquium Mathematicum 84 (2000), 485-493 DOI: 10.4064/cm-84/85-2-485-493


The orbit equivalence of type $III_{0}$ 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 $III_{0}$ cocycles with values in Abelian groups.


  • Alexandre Danilenko
  • Toshihiro Hamachi

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