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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\partial f \subset g + \gamma \mathbb{B}$$\end{document} around x entails that, for any γ′]0; γ[, f − g is γ′∈- Lipschitz continuous on an appropriate neighborhood of x.