Convex Representatives of the Value Function and Aumann Integrals in Normed Spaces

Convex representatives are proposed for the value function of an infinite-dimensional constrained nonconvex variational problem. All involved variables in this problem take their values (possibly infinite dimension, not necessarily separable or complete) normed spaces, while associated measure can be any $\sigma$-finite, nonnegative, and nonatomic complete measure. This particular shows that closure hull nonconvex) is always convex, as long sense integral within cone-valued functional constraint given type appropriately determined. Correspondingly, similar convexity properties Aumann general spaces dimension established. Applications a fairly positively homogeneous framework.