The universal asymptotic realization of integral constraints and constructions of extension in the class of finitely additive measures

The problem of keeping integral constraints is considered. The correct extension of the initial problem is constructed. The space of generalized elements consists of finitely additive measures of bounded variation which are weakly absolutely continuous with respect to a given measure space. The asymptotic equivalence of many variants of perturbations of integral constraints is discussed in terms of admissible sets. Applications to control problems are considered.