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

• Autorzy: Alexandre I. Danilenko , Toshihiro Hamachi
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 84/85
• Numer: 2
• Strony: 485-493

Daty

wydano

2000

otrzymano

1999-09-22

poprawiono

2000-03-15

Twórcy

autor

Alexandre I. Danilenko

• Department of Mechanics and Mathematics, Kharkov National University, Freedom square 4, Kharkov, 61077, Ukraine

autor

Toshihiro Hamachi

• Graduate School of Mathematics, Kyushu University, Ropponmatsu Chuo-ku, Fukuoka, 810-8560, Japan

Bibliografia

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