  As established by R T. Rockafellar, real valued convex-concave functions are
generically differentiable. It this paper we shall show that for a
convex-concave function defined on an open convex set $C \times D,$ there exist
dense subsets ${\cal N}$ of $C$ and ${\cal M}$ of $D$ such that the partial
derivative with respect to the first variable (resp. second variable) exists on
${\cal N} \times D$ (resp. $C \times {\cal M}$) and therefore the function is
differentiable on ${\cal N} \times {\cal M}$. This is an interesting property
of convex-concave functions and it does not hold for convex-convex functions.
As an immediate application we recover the generic single-valuedness of
monotone operators.
