{"product_id":"9783540226031","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eKechris, Alexander; Miller, Benjamin D.\u003c\/h2\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2004-08-26\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540226031\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/b99421\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 138\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":45369689538700,"sku":"9783540226031","price":40.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540226031.jpg?v=1775673802","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783540226031","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}