Weakly isomorphic transformations that are not isomorphic

Summary A new method for construction of transformations T_i: (X_i, B_i, _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 Sⁱ₁xSⁱ₂x...,, where : XZ₂ is a cocycle, S belongs to the centralizer of T and T is an ergodic translation on a compact, monothetic group X.