Some results on integration of subdifferentials

The integration of ∂*-subdifferentials, a class of subdifferentials which includes the lower Dini subdifferential, the Frechlet subdifferential and the m-subdifferential are studied. It is proved that if lower semicontinuous functions f:X→R, g:X→(-∞,∞] are such that g-f is lower semicontinuous on a nonempty open convex subset U of X, and for each x in U, ∂*f(x) union ∂*(-f)(x) is nonempty and bounded, then g differs from f by a constant on U. This result serves to unify and extend several results in the literature.