Lecture Notes in Mathematics

Topics in Orbit Equivalence

Authors: Kechris, Alexander, Miller, Benjamin D.

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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.

Table of contents (5 chapters)

  • I. Orbit Equivalence

    Kechris, Alexander S. (et al.)

    Pages 1-6

  • II. Amenability and Hyperfiniteness

    Kechris, Alexander S. (et al.)

    Pages 7-53

  • III. Costs of Equivalence Relations and Groups

    Kechris, Alexander S. (et al.)

    Pages 55-128

  • References

    Kechris, Alexander S. (et al.)

    Pages 129-130

  • Index

    Kechris, Alexander S. (et al.)

    Pages 131-134

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-44508-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-22603-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topics in Orbit Equivalence
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1852
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-44508-1
DOI
10.1007/b99421
Softcover ISBN
978-3-540-22603-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 138
Topics