Problems concerning
the approximation of convex valued multifunctions by continuous ones are
considered. Approximation results of the type obtained by Gel’man, Cellina,
and Hukuhara for Pompeiu-Hausdorff upper semicontinuous multifunctions
are shown to hold for some larger classes of multifunctions. Moreover, it is
proved that Pompeiu-Hausdorff semicontinuous multifunctions, with convex
bounded values, are continuous almost everywhere (in the sense of the Baire
category). As an application, an alternative proof is given of Kenderov’s
theorem stating that a maximal monotone operator is almost everywhere
single-valued.
