Absolute continuity of stable foliations for systems on Banach spaces

We prove the absolute continuity of stable foliations for C ^1,α maps of Banach spaces satisfying a globally defined infinitesimal invariant cones condition. Proofs of regularity for center and stable manifolds needed for the main theorem are included. Our results are applicable to dynamical systems generated by ordinary, partial, or functional differential equations, including non-autonomous differential equations that are periodic in time.