Countable Abelian Group Actions

and

Hyperfinite Equivalence Relations
colorful horizontal rule

Su Gao and Steve Jackson

Abstract

We prove that a Borel action of any countable abelian group gives rise to a hyperfinite equivalence relation.

Table of Contents

  1. Preliminaries

  2. Clopen marker sets

  3. Regular marker regions

  4. An application of regular marker regions

  5. Orthogonal marker regions

  6. Hyperfiniteness of F(Z<ω)

  7. The non-free part

  8. Actions of countable abelian groups

  9. Continuous embeddings into E0

  10. Open problems and further remarks

 

  

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