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It is proven that a microcanonical Gibbs measure on a classical discrete lattice system is a mixture of canonical Gibbs measures, provided the potential is “approximately periodic,” has finite range and possesses a commensurability property. No periodicity is imposed on the measure. When the potential is not approximately periodic or does not have the commensurability property, the inclusion does not hold.

Discrete lattice systems and the equivalence of microcanonical, canonical and grand canonical Gibbs states