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 Let E be an ergodic endomorphism of the Lebesgue probability space X, ℱ, μ. It gives rise to a decreasing sequence of σ-fields $ℱ,E^{-1}ℱ,E^{-2}ℱ,...$ A central example is the one-sided shift σ on $X={0,1}^{\mathbb{N}}$ with $\frac{1}{2},\frac{1}{2}$ product measure. Now let T be an ergodic automorphism of zero entropy on (Y, ν). The [I|T] endomorphismis defined on (X× Y, μ× ν) by $(x,y)\to (\sigma \left(x\right),T^{x\left(1\right)}\left(y\right))$. Here ℱ is the σ-field of μ× ν-measurable sets. Each field is a two-point extension of the one beneath it. Vershik has defined as “standard” any decreasing sequence of σ-fields isomorphic...