Closedness in the weak topology of the dual pair \(L^{1,C}\). (English) Zbl 0412.46040


46G05 Derivatives of functions in infinite-dimensional spaces
46E27 Spaces of measures
Full Text: DOI


[1] Brézis, H., Intégrales convexes dans les espaces de Sobolev, Israel J. Math., 13, 9-23 (1972) · Zbl 0249.46017
[2] Castaing, C.; Valadier, M., Convex Analysis and Measurable Multifunctions, (Lecture in Mathematics No. 580 (1977), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0346.46038
[3] Ioffe, A. D., Sur la semi-continuité des fonctionnelles intégrales, C. R. Acad. Sci. Paris, 284, 807-809 (1977) · Zbl 0348.49009
[4] Ioffe, A. D., On lower semicontinuity of integral functionals, I, SIAM J. Contr. Optimization, 15, 521-538 (1977) · Zbl 0361.46037
[5] Michael, E., Continuous selections, I, Ann. of Math., 63, No. 2, 361-382 (1956) · Zbl 0071.15902
[6] Olech, C., The characterization of the \(weak^∗\) closure of certain sets of integrable functions, SIAM J. Contr., 12, No. 2, 311-318 (1974) · Zbl 0296.46040
[7] Olech, C., A necessary and sufficient condition for lower semicontinuity of certain integral functionals, (Mathematical structures, Computational Mathematics, Mathematical Modelling (1975)), 373-379, Sofia
[8] Olech, C., Existence theory in optimal control problem: The underlying ideas, (International Conference on Differential Equations (1975), Academic Press: Academic Press New York), 612-635 · Zbl 0353.49013
[9] Olech, C., Existence theory in optimal control, (Control Theory and Topics in Functional Analysis, Vol. I (1976), International Atomic Energy Agency: International Atomic Energy Agency Vienna), 291-328 · Zbl 0353.49014
[10] Rockafellar, R. T., Convex Analysis (1970), Princeton Univ. Press: Princeton Univ. Press Princeton, N. J · Zbl 0202.14303
[11] Rockafellar, R. T., Integrals which are convex functionals, II, Pacific J. Math., 39, 439-469 (1971) · Zbl 0236.46031
[12] Rockafellar, R. T., Integral functionals, normal integrals and measurable selections, (Gossez, J. P., Nonlinear Operators and the Calculus of Variations. Nonlinear Operators and the Calculus of Variations, Lecture Notes in Mathematics No. 543 (1976), Springer-Verlag: Springer-Verlag Berlin), 157-207 · Zbl 0374.49001
[13] Sainte-Beuve, M.-F., Some topological properties of vector measures with bounded variations and its applications, Ann. Mat. Pura Appl., 116, 317-379 (1978) · Zbl 0379.46038
[14] Sainte-Beuve, M.-F., Sur l’adhérence de certains ensembles de fonctions vectorielles intégrables, (Sém. d’An. Convexe Montpellier No. 6 (1974)) · Zbl 0353.46033
[15] Sainte-Beuve, M.-F., Propriétés topologiques des mesures vectorielles et quelques applications, (Sém. d’An. Convexe Montpellier No. 2 (1975)) · Zbl 0351.46032
[16] Sainte-Beuve, M.-F., Complément sur les applications des propriétés topologiques des mesures vectorielles, (Sém. d’An. Convexe Montpellier No. 5 (1975)) · Zbl 0351.46033
[17] Nouguès-Sainte-Beuve, M.-F., Semi-continuité inférieure de certaines fonctionnelles intégrales, (Sém. d’An. Convexe Montpellier No. 7 (1976)) · Zbl 0372.49007
[18] Sainte-Beuve, M.-F., Propriétés topologiques des mesures vectorilles et applications, C. R. Acad. Sci. Paris, 280, 881-884 (1975) · Zbl 0302.28008
[19] Sainte-Beuve, M.-F., Mesures vectorielles à variation bornée et représentation intégrale, (Costé, A., Intégration vectorielle et multivoque. Intégration vectorielle et multivoque, Actes du Colloque de Caen, Offilib, Paris (1975)) · Zbl 0346.28006
[20] Tran cao Nguyen; Tran cao Nguyen
[21] Valadier, M., Fermeture, régularisée s.c.i. et bipolaire vagues, C. R. Acad. Sci. Paris, 284, 1025-1027 (1977) · Zbl 0351.46034
[22] Valadier, M., Fermeture étroite et bipolaire vague, (Sém. d’An. Convexe Montpellier No. 6 (1977)) · Zbl 0377.46036
[23] Tran cao Nguyen; Tran cao Nguyen
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