  We give a heuristic method to solve explicitly for an absolutely continuous
invariant measure for a piecewise differentiable, expanding map of a compact
subset $I$ of Euclidean space $R^d$. The method consists of constructing a skew
product family of maps on $I\times R^d$, which has an attractor. Lebesgue
measure is invariant for the skew product family restricted to this attractor.
Under reasonable measure theoretic conditions, integration over the fibers
gives the desired measure on $I$. Furthermore, the attractor system is then the
natural extension of the original map with this measure. We illustrate this
method by relating it to various results in the literature.
