Differentiability of Lipschitz maps from metric measure spaces to Banach   spaces with the Radon Nikodym property
  We prove the differentiability of Lipschitz maps X-->V, where X is a complete metric measure space satisfying a doubling condition and a Poincar\'e inequality, and V is a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direction of tangent vectors to suitable rectifiable curves. 
Jeff Cheeger and Bruce Kleiner