The orbit equivalence of type 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 cocycles with values in Abelian groups.
@article{bwmeta1.element.bwnjournal-article-cmv84i2p485bwm,
author = {Alexandre Danilenko and Toshihiro Hamachi},
title = {On measure theoretical analogues of the Takesaki structure theorem for type III factors},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {485-493},
zbl = {1006.37006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv84i2p485bwm}
}
Danilenko, Alexandre; Hamachi, Toshihiro. On measure theoretical analogues of the Takesaki structure theorem for type III factors. Colloquium Mathematicae, Tome 84/85 (2000) pp. 485-493. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i2p485bwm/
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