Abstract
The grand canonical Gibbs states for a system from classical statistical mechanics can be defined as the probability measures on an appropriate phase space which have certain specified conditional probabilities. These conditional probabilities are with respect to a family of σ-algebras associated with subsets of the space in which the system lies. If different families of σ-algebras are used then canonical and microcanonical Gibbs states are obtained. The relationship between these different Gibbs states is studied and, subject to various conditions, it is shown that each canonical and microcanonical Gibbs state can be written as a convex mixture of grand canonical Gibbs states.
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