Skip to main content

Topological property of the profile of a measurable multifunction with compact convex values

Part of the Lecture Notes in Mathematics book series (LNM,volume 580)

Keywords

  • Convex Compact
  • Radon Measure
  • Vector Measure
  • Positive Radon Measure
  • Empty Convex

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography of Chapter IV

  1. ALFSEN, E.M.-Compact convex sets and boundary integrals. Springer-Verlag. Berlin Heidelberg New York 1971.

    CrossRef  MATH  Google Scholar 

  2. ARKIN, V.I.-LEVIN, V.L.-Convexity of values of vector integrals theorems on measurable choices and variationals problems. Russian Math. Surveys 27, 21–85 (1972).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. BENAMARA, M.-Sections extrémales d'une multi-application. C.R. Acad. Sc. Paris 278, 1249–1252 (1974).

    MathSciNet  MATH  Google Scholar 

  4. Points extrémaux multi-applications et fonctionnelles intégrales. Thèse de 3o cycle, Grenoble (1975).

    Google Scholar 

  5. BERGE, C.-Espaces topologiques. Fonctions multivoques. Dunod 1958.

    Google Scholar 

  6. BLACKWELL, D.-The range of certain vector integrals. Proc. Amer. Math. Society 2, 390–395 (1951).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. BOURBAKI, N.-Topologie générale. Chapitre 9. 2ème édition. Hermann Paris 1958.

    Google Scholar 

  8. -Intégration sur les espaces topologiques séparés. Chapitre 9 Hermann Paris 1969.

    Google Scholar 

  9. CASTAING, Ch.-Sur les multi-applications mesurables. Revue d'Informatique et de Recherche opérationnelle 1, 91–126 (1967).

    MathSciNet  MATH  Google Scholar 

  10. Sur la mesurabilité du profil d'un ensemble convexe compact variant de façon mesurable. Collège Scientifique Universitaire Perpignan (1968). Polycopié.

    Google Scholar 

  11. -Sur une nouvelle extension du théorème de Ljapunov. C.R. Acad. Sc. Paris 264, 333–336 (1967).

    MathSciNet  MATH  Google Scholar 

  12. -Application d'un théorème de compacité à un résultat de désintégration des mesures. C.R. Acad. Sc. Paris 270, 1732–1735 (1970).

    MathSciNet  MATH  Google Scholar 

  13. CHOQUET, G.-MEYER, P.A.-Existence et unicité des représentations intégrales dans les convexes compacts quelconques. Ann. Inst. Fourier (Grenoble) 13, 139–154 (1963).

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. DUNFORD, N.-SCHWARTZ, J.T.-Linear operators. Part. I. Interscience 1964.

    Google Scholar 

  15. DVORETZKY, A.-WALD, A.-WOLFOWITZ, J.-Relations among certain ranges of vector measures. Pacific J. Math. 1, 59–74 (1951).

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. GODET-THOBIE, C.-Sur les multimesures de transition. C.R. Acad. Sc. Paris 278, 1367–1369 (1974) et exposé no 5, Séminaire d'Analyse convexe Montpellier (1974).

    Google Scholar 

  17. GHOUILA HOURI, A.-Sur la généralisation de la notion de commande d'un système guidable. Revue d'Informatique et de recherche opérationnelle 4, 7–32 (1967).

    MathSciNet  Google Scholar 

  18. HALMOS, P.R.-The range of a vector measure. Bull. Amer. Math. Soc. 54, 416–421 (1948).

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. KARLIN, S.-On extreme points of vector functions. Proc. Amer. Math. Society 4, 603–610 (1953).

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. KARLIN, S.-STUDDEN, W.J.-Tchebycheff systems; with applications in Analysis and Statistics. John Wiley 1966.

    Google Scholar 

  21. KELLERER, H.G.-Bemerkung zn einen satz von H. Richter. Archiv. der Math. 15, 204–207 (1964).

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. KINGMAN, J.F.C.-ROBERTSON, A.P.-On a theorem of Liapounoff, J. of London Math. Soc. 43, 347–351 (1968).

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. LINDENSTRAUSS, J.-A shorf proof of Liapounoff's convexity theorem. J. of Math. and Mechanics 15, 971–972 (1966).

    MathSciNet  MATH  Google Scholar 

  24. LJAPUNOV, A.-Sur les fonctions-vecteurs complètement additives. Bull. Acad. Sci. URSS sér. Math. 4, 465–478 (1940).

    Google Scholar 

  25. MEYER, P.A.-Probabilités et Potentiel. Hermann 1966.

    Google Scholar 

  26. NEVEU, J.-Bases mathématiques du calcul des probabilités. Masson 1964.

    Google Scholar 

  27. OLECH, C.-Extremal solutions of a control system. J. Differential equations 2, 74–101 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. SAINTE-BEUVE, M.F.-On the extension of Von Neumann-Aumann's theorem. J. Functional Analysis 17, 112–129 (1974).

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. STRASSEN, V.-The existence of probability measures with given marginals. Ann. Math. Stat. 36, 423–439 (1965).

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. VALADIER, M.-Contribution à l'analyse convexe. Thèse Faculté des Sciences (Paris) (1970).

    Google Scholar 

  31. WARGA, J.-Optimal control of Differential and Functional Equations, Academic Press, New York 1972.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1977 Springer-Verlag Berlin · Heidelberg

About this chapter

Cite this chapter

Castaing, C., Valadier, M. (1977). Topological property of the profile of a measurable multifunction with compact convex values. In: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol 580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087689

Download citation

  • DOI: https://doi.org/10.1007/BFb0087689

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08144-9

  • Online ISBN: 978-3-540-37384-1

  • eBook Packages: Springer Book Archive