04202nam 22008895 450 99646649890331620200706224009.03-540-44508-010.1007/b99421(CKB)1000000000231441(SSID)ssj0000327303(PQKBManifestationID)11230137(PQKBTitleCode)TC0000327303(PQKBWorkID)10301510(PQKB)11511844(DE-He213)978-3-540-44508-1(MiAaPQ)EBC6297042(MiAaPQ)EBC5591193(Au-PeEL)EBL5591193(OCoLC)56530431(PPN)155227343(EXLCZ)99100000000023144120121227d2004 u| 0engurnn|008mamaatxtccrTopics in Orbit Equivalence[electronic resource] /by Alexander Kechris, Benjamin D. Miller1st ed. 2004.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2004.1 online resource (X, 138 p.) Lecture Notes in Mathematics,0075-8434 ;1852Bibliographic Level Mode of Issuance: Monograph3-540-22603-6 Includes bibliographical references (pages 129-130) and index.Preface -- I. Orbit Equivalence -- II. Amenability and Hyperfiniteness -- III. Costs of Equivalence Relations and Groups -- References -- Index.This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.Lecture Notes in Mathematics,0075-8434 ;1852Mathematical analysisAnalysis (Mathematics)Mathematical logicFunctions of real variablesDynamicsErgodic theoryHarmonic analysisTopologyAnalysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Mathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Real Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12171Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XAbstract Harmonic Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12015Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28000Mathematical analysis.Analysis (Mathematics).Mathematical logic.Functions of real variables.Dynamics.Ergodic theory.Harmonic analysis.Topology.Analysis.Mathematical Logic and Foundations.Real Functions.Dynamical Systems and Ergodic Theory.Abstract Harmonic Analysis.Topology.515.48Kechris Alexanderauthttp://id.loc.gov/vocabulary/relators/aut60944Miller Benjamin Dauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996466498903316Topics in orbit equivalence262230UNISA