On the characterisation of Asplund spaces

Abstract A Banach space is an Asplund space if every continuous convex function on an open convex subset is Fréchet differentiable on a dense G 8 subset of its domain. The recent research on the Radon-Nikodým property in Banach spaces has revealed that a Banach space is an Asplund space if and only if every separable subspace has separable dual. It would appear that there is a case for providing a more direct proof of this characterisation.