Generic Fr´echet Differentiability of Convex Functions on Non-Asplund Spaces

Let f be a continuous convex function on a Banach space E. This paper shows that every proper convex function g on E with gFf is generically Fr´echet differentiable if and only if the image of the subdifferential map ­ f of f has the Radon]Nikod´ym property, and in this case it is equivalent to showing that the image of ­ f is separable on each separable subspace of E.