  We show that for a $\mathbb{Z}^{l}$-action (or $(\N\cup\{0\})^l$-action) on a
non-empty compact metrizable space $\Omega$, the existence of a affine space
dense in the set of continuous functions on $\Omega$ constituted by elements
admitting a unique equilibrium state implies that each invariant measure can be
approximated weakly$^*$ and in entropy by a sequence of measures which are
unique equilibrium states.
