Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows
T. Downarowicz, Y. Lacroix (1998)
Studia Mathematica
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Let be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of is Borel isomorphic to an almost 1-1 extension of . Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly...