The structure and regularity of the stable and unstable foliations, along with the regularity of the measure along these foliations, play fundamental roles in many arguments in dynamics. I will point out some of the important features of both foliations and measures in a sketch of the Hopf argument for ergodicity in hyperbolic systems, and then describe some pathological phenomena that can arise for partially hyperbolic systems. I will assume some basic familiarity with measure theory. Speaker(s): Salman Siddiqi (UM)