We're referencing Yakov Pesin's "Dimension Theory in Dynamical Systems" in an effort to compute the Hausdorff dimension of a particular invariant set $\Lambda$ of a hyperbolic toral automorphism. Theorem 22.1 in the text gives the dimension of the set in terms of the measure-theoretic entropy with respect to the unique equilibrium measure. This equilibrium measure is guaranteed to be unique as the set $\Lambda$ is locally maximal.

The problem we're running into is that the sets we consider need not be locally maximal. However, again from Pesin theorem A2.2 we know that equilibrium measures will exist for our system. This leads to the question: Will the equation given in theorem 22.1 work if the integration is taken with respect to one of these measures?