Solution of Monge-Amp\`ere Equation on Wiener Space for log-concave   measures: General case
  We show the existence of the strong solutions of the Monge-Ampere equation for the log-concave measures without any regularity assumption. In particular the measures with density of the form $\exp -f$, where $f$ is an $H$-convex function which may take the value $\infty$ on a set of positive measure are included. 
Denis Feyel and A.S. Ustunel