  We prove the equivalence between the existence of a non-trivial hitting time
statistics law and Extreme Value Laws in the case of dynamical systems with
measures which are not absolutely continuous with respect to Lebesgue. This is
a counterpart to the result of the authors in the absolutely continuous case.
Moreover, we prove an equivalent result for returns to dynamically defined
cylinders. This allows us to show that we have Extreme Value Laws for various
dynamical systems with equilibrium states with good mixing properties. In order
to achieve these goals we tailor our observables to the form of the measure at
hand.
