On the regular representation of measures
  We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class $C^k$. The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular representability. 
J\"urgen Jost, Rostislav Matveev, Jacobus W. Portegies, Christian S.   Rodrigues
math.DG math.AP math.DS