Localized variational principle for non-Besicovitch metric spaces

We consider the localized entropy of a point w∈Rmw∈Rm which is computed by considering only those (n,ε)(n,ε)-separated sets whose statistical sums with respect to an m-dimensional potential Φ are “close” to a given value w. Previously, a local version of the variational principle was established for systems on non-Besicovitch compact metric spaces. We extend this result to all compact metric spaces.