  We prove that for certain partially hyperbolic skew-products, non-uniform
hyperbolicity along the leaves implies existence of a finite number of ergodic
absolutely continuous invariant probability measures which describe the
asymptotics of almost every point. The main technical tool is an extension for
sequences of maps of a result of de Melo and van Strien relating hyperbolicity
to recurrence properties of orbits. As a consequence of our main result, we
also obtain a partial extension of Keller's theorem guaranteeing the existence
of absolutely continuous invariant measures for non-uniformly hyperbolic one
dimensional maps.
