On the distribution of long-term time averages on symbolic space

The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete ac count in the case of symbolic spaces, including subshifts of finite type. W e relate the pressure of an interaction function Phi to its long-term time averages through the Hausdorff and packing dimensions of the subsets on whi ch Phi has prescribed long-term time-average values. Functions Phi with val ues in R-d are considered. For those Phi depending only on finitely many sy mbols, we get complete results, unifying and completing many partial result s.