Relative entropy, dimensions and large deviations for g-measures

We prove large-deviation results for empirical measures, with respect to an arbitrary g-measure on a subshift of finite type, by using an ergodic theorem for relative entropy we establish. Extending some results of Cajar on Billingsley dimensions to g-measures, we relate the relative entropy to the dimensions of saturated sets. This allows a dimensional interpretation of the large-deviation results and the study of the set of non-generic points which are proved to be of full dimension.