Dense single-valuedness of monotone operators

It is shown that the set of points for which a monotone mappingT:X→X ^* from a separable Banach space into its dual is not single-valued has no interior; if dimX<∞ and intD(T)≠ϕ then the set has Lebesgue measure zero. Moreover, for accretive mappingsT:X→X from a separable Banach space into itself, the dimension of the set of points whose images contain balls of codimension not larger thank does not exceedk. Applications to convexity are given.