Summary
A new method for construction of transformations T i: (X i, B i, μ i) ↷, i=1,2, that are factors of each other but that are not measuretheoretically isomorphic is provided. This method uses ergodic product cocycles of the form ϕ∘S i 1xϕ∘S i 2x...,, where ϕ: X→Z 2 is a cocycle, S belongs to the centralizer of T and T is an ergodic translation on a compact, monothetic group X.
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Lemańczyk, M. Weakly isomorphic transformations that are not isomorphic. Probab. Th. Rel. Fields 78, 491–507 (1988). https://doi.org/10.1007/BF00353873
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DOI: https://doi.org/10.1007/BF00353873