  We consider some classes of piecewise expanding maps in finite dimensional
spaces having invariant probability measures which are absolutely continuous
with respect to Lebesgue measure. We derive an entropy formula for such
measures and, using this entropy formula, in some parametrized families we
present sufficient conditions for the continuity of that entropy with respect
to the parameter. We apply our results to a classical one-dimensional family of
tent maps and a family of two-dimensional maps which arises as the limit of
return maps when a homoclinic tangency is unfolded by a family of three
dimensional diffeomorphisms.
