For a translation invariant Gibbs measure v on the configuration space X of a lattice finite spin system, we consider the set Xμ of generic points. Using a Breiman type convergence theorem on the set X μ of generic points of an arbitrary translation invariant probability measure μ on X, we evaluate the Hausdorff dimension of the set Xμ with respect to any metric out of a wide class of "scale" metrics on X (including Billingsley metrics generated by Gibbs measures).
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics