Integration of Nonconvex Epi-Pointed Functions in Locally Convex Spaces

We extend results of R. Correa, Y. Garcia and A. Hantoute ["Integration formulas via the (Fenchel) subdifferential of nonconvex functions", Nonlinear Analysis 75(3) (2012) 1188-1201)] dealing with the integration of nonconvex epi-pointed functions using the Fenchel subdifferential. In this line, we prove that the classical formula of Rockafellar in the convex setting is still valid in general locally convex spaces for an appropriate family of nonconvex epi-pointed functions, namely those we call SDPD. The current integration formulas use the Fenchel subdifferential of the involved functions to compare the corresponding closed convex envelopes. Some examples of SDPD functions are investigated. This analysis leads us to approach a useful family of locally convex spaces, referred to as the SDPD, having an RNP-like property