  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.
