Closed Subgroups Generated by Generic Measure Preserving Transformations

The uploaded paper proves that for a comeager set of T in Aut(γ), no continuous homomorphism from any L0(ν, 𝕋) has T in its image (Theorem 1.1), via a contradiction that builds an ergodic boolean L0-action and confronts spectral constraints from the representation theory of L0 with generic spectral independence of powers of T . The candidate’s solution outlines the same approach: contradiction, boolean action, Solecki’s 2014 representation classification, and generic spectral independence. Minor issues are terminological (mislabeling Theorem 5.1 as an ergodic theorem) and omission of some standard reductions (splitting ν and using openness to pass to L0(λ, 𝕋)), but the logical core matches the paper’s proof and conclusion .