  We prove a generalization of a so called "invariance principle" for partially
hyperbolic diffeomorphisms: if an invariant probability measure has all its
center Lyapunov exponents equal to zero then the measure admits a center
disintegration that is invariant by stable and unstable holonomies. This was
known for systems admitting a foliation by compact center leaves, and we extend
it to a larger class which contains discretized Anosov flows.
  We use our result to classify measures of maximal entropy and study physical
measures for perturbations of the time-one map of Anosov flows.
