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Theorem 1.1. There exists an ergodic invertible measure-preserving transformation (X,μ,T) of a standard nonatomic probability space such that h_μ(T)=0 and (X,μ,T) is not measurably conjugate, on invariant conull sets, to any C^∞ …

Theorem 1.1. There exists an ergodic invertible measure-preserving transformation (X,μ,T) of a standard nonatomic probability space such that h_μ(T)=0 and (X,μ,T) is not measurably conjugate, on invariant conull sets, to any C^∞ diffeomorphism of a compact finite-dimensional manifold preserving a strictly positive smooth probability density. The manifold may have smooth boundary and need not be orientable.