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This book deals with the construction of correct extensions of extremal problems including problems of multicriterial optimization and more general problems of optimization with respect to a cone. These questions need to be investigated, as extremal problems may be unstable with respect to either an attainable result, or with respect to solutions providing an optimal result (precisely or approximately). The methods of qualitative stability and asymptotically insensitive analysis proposed here are particularly applicable to problems of optimal control with integrally constrained openloop controls. A nontraditional mathematical tool using elements of finitely-additive measure theory is applied, which necessitated special research concerned with approximative analogues of the Radon-Nikodym property. These abstract constructions do, however, address the essence of the problem at hand, and may find other applications as well. Audience: This volume will be useful to specialists and graduate students whose fields of interest include control theory and its applications, measure integration, functional analysis, optimal control, fuzzy sets and fuzzy logic, and general topology.