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  • © 2004

Topics in Orbit Equivalence

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1852)

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Table of contents (5 chapters)

  1. Front Matter

    Pages N2-X
  2. I. Orbit Equivalence

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 1-6
  3. II. Amenability and Hyperfiniteness

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 7-53
  4. III. Costs of Equivalence Relations and Groups

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 55-128
  5. References

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 129-130
  6. Index

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 131-134
  7. Back Matter

    Pages 129-135

About this book

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.

Keywords

  • Equivalence
  • amenability
  • cost
  • equivalence relations
  • hyperfiniteness
  • orbit equivalence
  • set
  • set theory

Bibliographic Information

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions