Random Multifunctions as Set Minimizers of Infinitely Many Differentiable Random Functions

Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers an infinitely many differentiable normal integrand, which preserves convexity multifunction. This result is extended version work done by Azagra and Ferrera (Proc Am Math Soc 130(12):3687–3692, 2002). We provide several applications this to approximation multifunctions integrands. The paper ends with a characterization integrable selections measurable integral function.