Ricci curvature on mm-spaces:
http://www.math.lsa.umich.edu/~lott/transport062306.pdf
http://www.math.lsa.umich.edu/~lott/papers.html
http://arxiv.org/abs/math.PR/0701886
A Sheaf Theoretic Approach to Measure Theory
http://etd.library.pitt.edu/ETD/available/etd-04202006-065320/unrestricted/Matthew_Jackson_Thesis_2006.pdf
BRWG