Balder, E. J. A general denseness result for relaxed control theory. (English) Zbl 0544.49008 Bull. Aust. Math. Soc. 30, 463-475 (1984). 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 Cited in 25 Documents 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. Keywords:elimination of relaxation; relaxed control; integrals of multifunctions PDF BibTeX XML Cite \textit{E. J. Balder}, Bull. Aust. Math. Soc. 30, 463--475 (1984; Zbl 0544.49008) Full Text: DOI References: [1] Billingsley, Convergence of probability measures (1968) · Zbl 0172.21201 [2] Castaing, Convex analysis and measurable multi-functions 580 (1977) · doi:10.1007/BFb0087685 [3] Balder, Statistics and decisions [4] Balder, J. Multivariate Anal [5] DOI: 10.1137/0322035 · Zbl 0549.49005 · doi:10.1137/0322035 [6] DOI: 10.1016/0022-247X(79)90235-X · Zbl 0434.49007 · doi:10.1016/0022-247X(79)90235-X [7] DOI: 10.1016/0022-247X(65)90049-1 · Zbl 0163.06301 · doi:10.1016/0022-247X(65)90049-1 [8] Warga, Optimal control of differential and functional equations (1972) [9] DOI: 10.1007/BF02413878 · Zbl 0379.46038 · doi:10.1007/BF02413878 [10] Neveu, Bases mathématiques du calcul des probabilitiés (1964) [11] Hildenbrand, Core and equilibria of a large economy (1974) · Zbl 0351.90012 [12] Ghouila-Houri, Rev. Franc. d’inf. Rech. Opér. 4 pp 7– (1967) [13] DOI: 10.1214/aoms/1177729689 · Zbl 0044.15003 · doi:10.1214/aoms/1177729689 [14] Chuong, Travaux duSeminaire d’analyse Convexe (1981) [15] Dellacherie, Pvobabilités et potentiel (1975) [16] Berliocchi, Bull. Soc. Math. 101 pp 129– (1973) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.