Almost 1-1 extensions of Furstenberg-Weiss type and test for amenability
Abstract
Let G G be an infinite residually finite group. We show that for every minimal equicontinuous Cantor system ( Z , G ) (Z,G) with a free orbit, and for every minimal extension ( Y , G ) (Y,G) of ( Z , G ) (Z,G) , there exist a minimal almost 1-1 extension ( X , G ) (X,G) of ( Z , G ) (Z,G) and a Borel equivariant map ψ : Y → X \psi :Y\to X that induces an affine bijection ψ ∗ \psi ^* between M ( Y , G ) \mathcal {M}(Y,G) and M ( X , G ) \mathcal {M}(X,G) , the spaces of invariant probability measures of ( Y , G ) (Y,G) and (
Fields of Study & Subjects
Advanced Operator Algebra Research
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Publication date
- 18 February 2026
- Language
- EN