A weakly second order differential structure on rectifiable metric   measure spaces
  We give the definition of angles on a Gromov-Hausdorff limit space of a sequence of complete n-dimensional Riemannian manifolds with a lower Ricci curvature bound. We apply this to prove there is a weakly second order differential structure on these spaces and prove there is a unique Levi-Civita connection allowing us to define the Hessian of a twice differentiable function. 
Shouhei Honda
math.DG math.MG