# On subrelations of ergodic measured type III equivalence relations

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 1, page 13-22
- ISSN: 0010-1354

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topDanilenko, Alexandre. "On subrelations of ergodic measured type III equivalence relations." Colloquium Mathematicae 84/85.1 (2000): 13-22. <http://eudml.org/doc/210792>.

@article{Danilenko2000,

abstract = {We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.},

author = {Danilenko, Alexandre},

journal = {Colloquium Mathematicae},

keywords = {orbit theory; ergodic relations},

language = {eng},

number = {1},

pages = {13-22},

title = {On subrelations of ergodic measured type III equivalence relations},

url = {http://eudml.org/doc/210792},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Danilenko, Alexandre

TI - On subrelations of ergodic measured type III equivalence relations

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 1

SP - 13

EP - 22

AB - We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.

LA - eng

KW - orbit theory; ergodic relations

UR - http://eudml.org/doc/210792

ER -

## References

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