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100   $a20121227d2004      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aTopics in Orbit Equivalence$b[electronic resource] /$fby Alexander Kechris, Benjamin D. Miller
205   $a1st ed. 2004.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004.
215   $a1 online resource (X, 138 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1852
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-22603-6 
320   $aIncludes bibliographical references (pages 129-130) and index.
327   $aPreface -- I. Orbit Equivalence -- II. Amenability and Hyperfiniteness -- III. Costs of Equivalence Relations and Groups -- References -- Index.
330   $aThis volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1852
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aMathematical logic
606   $aFunctions of real variables
606   $aDynamics
606   $aErgodic theory
606   $aHarmonic analysis
606   $aTopology
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005
606   $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015
606   $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aMathematical logic.
615  0$aFunctions of real variables.
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aHarmonic analysis.
615  0$aTopology.
615 14$aAnalysis.
615 24$aMathematical Logic and Foundations.
615 24$aReal Functions.
615 24$aDynamical Systems and Ergodic Theory.
615 24$aAbstract Harmonic Analysis.
615 24$aTopology.
676   $a515.48
700   $aKechris$b Alexander$4aut$4http://id.loc.gov/vocabulary/relators/aut$060944
702   $aMiller$b Benjamin D$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910144617803321
996   $aTopics in orbit equivalence$9262230
997   $aUNINA