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

Alexandre Danilenko; Toshihiro Hamachi

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 2, page 485-493
- ISSN: 0010-1354

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topDanilenko, Alexandre, and Hamachi, Toshihiro. "On measure theoretical analogues of the Takesaki structure theorem for type III factors." Colloquium Mathematicae 84/85.2 (2000): 485-493. <http://eudml.org/doc/210828>.

@article{Danilenko2000,

abstract = {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.},

author = {Danilenko, Alexandre, Hamachi, Toshihiro},

journal = {Colloquium Mathematicae},

keywords = {orbit equivalence; outer conjugacy; ergodic countable transformation group; ergodic discrete equivalence relation; cocycle},

language = {eng},

number = {2},

pages = {485-493},

title = {On measure theoretical analogues of the Takesaki structure theorem for type III factors},

url = {http://eudml.org/doc/210828},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Danilenko, Alexandre

AU - Hamachi, Toshihiro

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

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 2

SP - 485

EP - 493

AB - 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.

LA - eng

KW - orbit equivalence; outer conjugacy; ergodic countable transformation group; ergodic discrete equivalence relation; cocycle

UR - http://eudml.org/doc/210828

ER -

## References

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