The size of the Dini subdifferential

Given a lower semicontinuous function f : R-h --> R boolean OR {+infinity}, we prove that the points of R-h, where the lower Dini subdifferential cont ains more than one element, lie in a countable union of sets which are isom orphic to graphs of some Lipschitzian functions defined on Rh-1. Consequent ly, the set of all these points has a null Lebesgue measure.