Prépublication du DMI numéro 00-02 (23/01/2001)

INTEGRATION OF SUBDIFFERENTIALS OF LOWER SEMICONTINUOUS FUNCTIONS.
GEOFFROY, Michel - Groupe de Recherche de Mathématiques, Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex
JULES, Florence - Groupe de Recherche de Mathématiques, Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex
LASSONDE, Marc - Groupe de Recherche de Mathématiques, Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex

In 1993, Thibault and Zagrodny established a result recovering Rockafellar's integration theorem (dealing with convex functions) and also a characterization of Lipschitz functions. Our purpose is to provide a generalization of their statement involving an abstract notion of subdifferential in the sense of Lassonde. Indeed, the latter ensures a wider application field since it permits to apply our result to the smallest subdifferentials without considering limiting subdifferentials. Finally, we give a characterization of Lipshitz functions which yields a theorem of integration in the continuous setting.