Gibbs states on countable sets

In this chapter we will examine certain probability measures on P(S), the set of all subsets of S, where S is a countable set. We will be interested in the existence and uniqueness of measures satisfying certain properties. As before we will regard the points of S as sites, each of which can be either empty or occupied by a particle (or some other entity); the subset A ∈ P(S) will be regarded as describing the situation when the points of A are occupied and the points of S - A are empty. The elements of P(S) will sometimes be called configurations and the probability measures on P(S) that we will look at will describe the equilibrium distribution of the configurations of some model.

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