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dc.contributor.authorHjorth, G
dc.date.available2014-05-21T20:51:01Z
dc.date.issued2005-01-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000229438200005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=d4d813f4571fa7d6246bdc0dfeca3a1c
dc.identifier.citationHjorth, G. (2005). A converse to Dye's theorem. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 357 (8), pp.3083-3103. https://doi.org/10.1090/S0002-9947-04-03672-4.
dc.identifier.issn0002-9947
dc.identifier.urihttp://hdl.handle.net/11343/27839
dc.descriptionC1 - Refereed Journal Article
dc.description.abstract<p>Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper F 2"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">F</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">\mathbb {F}_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not universal for treeable in the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="less-than-or-equal-to Subscript upper B Baseline"> <mml:semantics> <mml:msub> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>B</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">\leq _B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ordering.</p>
dc.languageEnglish
dc.publisherAMER MATHEMATICAL SOC
dc.subjectPure Mathematics
dc.titleA converse to Dye's theorem
dc.typeJournal Article
dc.identifier.doi10.1090/S0002-9947-04-03672-4
melbourne.peerreviewPeer Reviewed
melbourne.affiliationThe University of Melbourne
melbourne.affiliation.departmentMathematics and Statistics
melbourne.source.titleTransactions of the American Mathematical Society
melbourne.source.volume357
melbourne.source.issue8
melbourne.source.pages3083-3103
melbourne.publicationid79513
melbourne.elementsid289788
melbourne.contributor.authorHJORTH, GREG
melbourne.internal.ingestnoteAbstract bulk upload (2017-07-20)
dc.identifier.eissn1088-6850
melbourne.accessrightsThis item is currently not available from this repository


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