Topics in Orbit Equivalence
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"Topics in Orbit Equivalence" by Alexander S. Kechris, Benjamin D. Miller is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
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.
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"Topics in Orbit Equivalence" by Alexander S. Kechris, Benjamin D. Miller is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Core Mathematics
Author: Alexander S. Kechris, Benjamin D. Miller
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
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.
| Author | Alexander S. Kechris, Benjamin D. Miller |
| Publisher | Springer Science & Business Media |
| Published | 2004-08-26 |
| ISBN-13 | 9783540226031 |
| Binding | Paperback |
| Pages | 148 |
| Language | English |
| Subjects | Computers |
| Topic | Core Mathematics |
| Series | Lecture Notes in Mathematics |
Format: Paperback
Length: 148 pages
Language: English
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