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＜電子ブック＞
Topics in Orbit Equivalence / by Alexander Kechris, Benjamin D. Miller
(Lecture Notes in Mathematics. ISSN:16179692 ; 1852)

版	1st ed. 2004.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2004
大きさ	X, 138 p : online resource
著者標目	*Kechris, Alexander author Miller, Benjamin D author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Mathematical logic LCSH:Functions of real variables LCSH:Dynamical systems LCSH:Harmonic analysis LCSH:Topology FREE:Analysis FREE:Mathematical Logic and Foundations FREE:Real Functions FREE:Dynamical Systems FREE:Abstract Harmonic Analysis FREE:Topology
一般注記	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 HTTP:URL=https://doi.org/10.1007/b99421

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