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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Orbit Equivalence of Minimal Actions of a Finitely Generated Abelian Group
verfasst von : Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
Erschienen in: Crossed Products of C*-Algebras, Topological Dynamics, and Classification
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In measurable dynamics, the study of orbit equivalence, initiated by Dye [19], was developed by Krieger [56], Ornstein–Weiss [73] and Connes–Feldman–Weiss [13] among many others in the amenable case. The strategy of their proofs consisted of showing that any amenable measurable equivalence relation is orbit equivalent to a hyperfinite measurable equivalence relation and classifying these ones. In the nonsingular case, the complete invariant of orbit equivalence is an ergodic flow, the so-called associated flow; see Krieger [56].