Prevalent uniqueness in ergodic optimisation

Abstract

One of the fundamental results of ergodic optimisation asserts that for any dynamical system on a compact metric space X X and for any Banach space of continuous real-valued functions on X X which embeds densely in C ( X ) C(X) there exists a residual set of functions in that Banach space for which the maximising measure is unique. We extend this result by showing that this residual set is additionally prevalent, answering a question of J. Bochi and Y. Zhang.