Measurable Riemannian structures associated with strong local Dirichlet   forms
  We introduce Riemannian-like structures associated with strong local Dirichlet forms on general state spaces. Such structures justify the principle that the pointwise index of the Dirichlet form represents the effective dimension of the virtual tangent space at each point. The concept of differentiations of functions is studied, and an application to stochastic analysis is presented. 
Masanori Hino
math.PR