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A general denseness result for relaxed control theory. (English) Zbl 0544.49008
Author’s summary: ”A result by the author on the elimination of randomization (or relaxation) for variational problems is partially extended and then used to obtain a very general result on the denseness of the set of original control functions in the set of relaxed control functions. Also, a slight extension of Aumann’s theorem on the integrals of multifunctions is shown to follow directly from the elimination result”.
Reviewer: C.Vinti

MSC:
49J45 Methods involving semicontinuity and convergence; relaxation
49J27 Existence theories for problems in abstract spaces
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
46A04 Locally convex Fréchet spaces and (DF)-spaces
46A50 Compactness in topological linear spaces; angelic spaces, etc.
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