Integration of primal lower nice functions in Hilbert spaces

In this paper, we obtain some integration results from subdifferential inclusions for primal lower nice functions by using the Moreau envelopes. A general result concerns an enlarged subdifferential inclusion. It says that, for g primal lower nice at x, the inclusion partial derivative f subset of partial derivativeg + gamma B around x entails that, for any gamma' epsilon]0; gamma[, the function f - g is gamma'- Lipschitz continuous on an appropriate neighborhood of x.