  We consider a class of piecewise hyperbolic maps from the unit square to
itself preserving a contracting foliation and inducing a piecewise expanding
quotient map, with infinite derivative (like the first return maps of Lorenz
like flows). We show how the physical measure of those systems can be
rigorously approximated with an explicitly given bound on the error, with
respect to the Wasserstein distance. We apply this to the rigorous computation
of the dimension of the measure. We present a rigorous implementation of the
algorithms using interval arithmetics, and the result of the computation on a
nontrivial example of Lorenz like map and its attractor, obtaining a statement
on its local dimension.
