Sequence Entropy Tuples and Mean Sensitive Tuples

The PDF proves SM^µ_n ⊂ SE^µ_n (Theorem 1.1), SE^µ_n ⊂ MS^µ_n for ergodic µ (Theorem 1.2), hence SE^µ_n = SM^µ_n = MS^µ_n when µ is ergodic (Corollary 1.3), and provides a non-ergodic counterexample where SM^µ_n ⊊ SE^µ_n (Theorem 1.4). See the paper’s statements and definitions, including the admissible-partition and Kronecker-factor setup, and Lemma 4.6 used in the non-ergodic construction . The candidate’s solution matches these results and quantifiers, and its proof sketches track the paper’s arguments (Kronecker algebra for Theorem 1.1 and the continuous disintegration/Birkhoff argument for Theorem 1.2) . Minor issues: the model mislabels theorem numbers (calling Theorem 1.1 “Theorem 1.4” and Theorem 1.2 “Theorem 1.5”) and presents a different but valid non-ergodic example; both are consistent with the paper’s claims.