BERNOULLI PROPERTY OF SUBADDITIVE EQUILIBRIUM STATES

The paper proves Bernoulli-ness for the stated subadditive equilibrium states by establishing measurable local product structure and then applying an abstract K + product-absolute-continuity ⇒ Bernoulli theorem, after invoking quasi-multiplicativity/bounded distortion and a prior K-property result. The candidate solution instead tries to short-circuit everything by appealing directly to Morris’s Bernoulli theorem for totally ergodic generalized matrix equilibrium states, but that theorem applies in the locally constant (matrix) setting, whereas the paper’s fiber-bunched Hölder cocycles are not assumed locally constant. Thus the model misapplies an external result; the paper’s argument is consistent and complete.