ON THE JEWETT-KRIEGER THEOREM FOR AMENABLE GROUPS

Weiss proves a slightly strengthened Jewett–Krieger theorem for amenable groups by combining: (i) a construction of a 0-dimensional topologically free model that is measure-isomorphic to the original action via the explicit coding F together with the product/graph embedding F̂: X → X×Ω₀ (Proposition 1), and (ii) the Frej–Huczek faces-of-simplices theorem to reach unique ergodicity and then restricting to the support for minimality (Theorem 1 → Corollary 1) . The candidate’s Step 1 incorrectly asserts that the coded factor Z (the topological support of the pushforward) is already measure-isomorphic to the original system; Weiss instead uses the factor-joining product X×Ω₀ specifically to achieve a measure isomorphism. Without this step, the Frej–Huczek reduction may deliver a uniquely ergodic model for a factor but not necessarily for the original action. Apart from this, the candidate’s outline aligns with Weiss’s use of Frej–Huczek and the final support restriction to obtain strict ergodicity .