Weak Gibbs and Equilibrium Measures for Shift Spaces

For a large class of irreducible shift spaces $X\subset\tA^{\Z^d}$, with $\tA$ a finite alphabet, and for absolutely summable potentials $\Phi$, we prove that equilibrium measures for $\Phi$ are weak Gibbs measures. In particular, for $d=1$, the result holds for irreducible sofic shifts.