Large deviations for empirical entropies of g-measures

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x(1)(n) using the entropy of the k-block empirical probability and letting k grow with n roughly like log n. We further assume that the, I distribution of the process is a g-measure. We prove large deviation principles for conditional, non-conditional and relative k(n)-block empirical entropies.