Abstract
We are interested here in the characterization on a symbolic space, of invariant Gibbs measures as equilibrium measures. The first result in this topic was obtained by Lanford and Ruelle (see for example [6]). This problem involves different objects that can all be defined by using the only amenability of the translation group and the only continuity of the local specification. We therefore tried to state our theorems in this general frame. Among the elements of our proof, there is the use of the information gain introduced by H. Follmer [1] and some arguments similar to those of C.J. Preston in [5]. But the amenability techniques that we widely develop in [2], [4] and [7] are decisive tools for getting the result. The corresponding problem for subshifts is not considered in the present paper so symbolic spaces are product spaces.
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