Ergodic optimization for generic continuous functions

Given a real-valued continuous function f defined on the phase space of a dynamical system, an invariant measure is said to be maximizing if it maximises the integral of f over the set of all invariant measures. Extending results of Bousch, Jenkinson and Bremont, we show that the ergodic maximizing measures of functions belonging to a residual subset of the continuous functions may be characterised as those measures which belong to a residual subset of the ergodic measures