Microcanonical distributions for lattice gases

In this article, a large deviation principle (cf. Theorem 1.3) for the empirical distribution functional is applied to prove a rather general version of Boltzmann's principle (cf. Theorem 3.5) for models with shift-invariant, finite range potentials. The final section contains an application of these considerations to the two dimensional Ising model at sub-critical temperature.The first two authors acknowledge support from, respectively, the grants NSF DMS-8802667 and NSF DMS-8913328 & DAAL 03-86-K-0171