Hostname: page-component-cb9f654ff-lqqdg Total loading time: 0 Render date: 2025-08-01T09:27:09.770Z Has data issue: false hasContentIssue false
  • English
  • Français

On uniformly bounded sequences in Orlicz spaces

Published online by Cambridge University Press:  17 April 2009

Erik J. Balder
Erik J. Balder
Affiliation:
Mathematical Institute, University of Utrecht, Utrecht, Netherlands
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A useful result for uniformly bounded sequences of functions in Orlicz spaces is generalised by means of a recent extension of Komlós' theorem. The same generalisation can also be proven differently, by means of Young measures.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 495 - 502
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Balder, E.J., ‘A general approach to lower semicontinuity and lower closure in optimal control theory’, SIAM J. Control Optim. 22 (1984), 570–598.CrossRefGoogle Scholar
[2]Balder, E.J., ‘Fatou's lemma in infinite dimensions’, J. Math. Anal. Appl. 116 (1988), 450–465.CrossRefGoogle Scholar
[3]Balder, E.J., ‘On Prohorov's theorem for transition probabilities’, Sém. Anal. Convexe 19 (1989), 9.1–9.11.Google Scholar
[4]Balder, E.J., ‘Infinite-dimensional extension of a theorem of Komlos’, Probab. Theory Related Fields 81 (1989), 185–188.CrossRefGoogle Scholar
[5]Balder, E.J., ‘New sequential compactness results for spaces of scalarly integrable functions’, J. Math. Anal. Appl. (1990) (to appear).CrossRefGoogle Scholar
[6]Balder, E.J., ‘Short proof of an existence result of V.L. Levin’, Bull. Polish Acad. Sci. Math. (to appear).Google Scholar
[7]Ball, J.M. and Murat, F., ‘Remarks on Chacon's biting lemma’, preprint Analyse Numérique, Université Pierre et Marie Curie, Paris, 1988.Google Scholar
[8]Brooks, J.K. and Chacon, R.V., ‘Continuity and compactness of measures’, Adv. in Math. 37 (1980), 16–26.CrossRefGoogle Scholar
[9]Castaing, C., ‘Sur la décomposition de Slaby. Applications aux problèmes de convergence en probabilités, économie mathématique, théorie du contrôle, minimisation’, Sém. Anal. Convexe 19 (1989) (to appear).Google Scholar
[10]Gaposhkin, V.F., ‘Convergence and limit theorems for sequences of random variables’, Theory Prob. and Appl. 17 (1972), 379–400.CrossRefGoogle Scholar
[11]Garling, D.J.H., ‘Subsequence principles for vector–valued random variables’, Math. Proc. Cambridge Philos Soc. 86 (1979), 301–311.CrossRefGoogle Scholar
[12]Giner, E., Espaces Integraux de Type Orlicz' (Thèse, Université des Sciences et Techniques du Languedoc, Perpignan, 1977).Google Scholar
[13]Levin, V.L., ‘Extremal problems with convex functionals that are lower semicontinuous with respect to convergence in measure Dokl. Akad. Nauk SSSR’ 224, pp. 1256–1259. Soy. Math. Dokl. 16 (1976), 1384–1388).Google Scholar
[14]Levin, V.L., Convex Analysis, (in Russian), Nauka, Moscow, (1985).Google Scholar
[15]Valadier, M., ‘Convergence en mesure et optimisation (d'après Levin)’, Sém. Anal. Convexe 6 (1976), 14.1–14.9.Google Scholar
[16]Valadier, M., Young Measures (CIME Lecture Notes, 1989). (to appear).Google Scholar