be a finite atomless measure space and
be convex real-valued set functions defined on a convex subfamily
. Consider an optimization problem as follows: (P) Minimize
. The authors prove a theorem of Moreau-Rockafellar type for set functions, and then use the theorem to prove a Kuhn-Tucker type condition for an optimal solution of the minimization problem (P) for real valued set functions. If the set functions are vector-valued, the Fritz John type condition for an optimum of the multiobjective minimization problem (P) is established.