Skip to main content
Log in

Measurable selectors of multifunctions and applications

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. R. J. Aumann, Measurable utility and the measurable choice theorem, Proc. Internat. Colloq., La Décision, C.N.R.S., Aix-en-Provence, 1967.

  2. N. Bourbaki,General Topology, Part 2, Addison-Wesley, Reading, Mass., 1966.

    Google Scholar 

  3. C. Castaing, Sur les multi-applications mesurables,Rev. Français Informat. Recherche Opérat., No.1 (1967), 91–126.

    Google Scholar 

  4. R. Datko, Measurability properties of set-valued mappings in a Banach space,SIAM J. Control 8 (1970), 226–238.

    Google Scholar 

  5. G. Debreu, Integration of correspondences,Proc. 5th Berkeley Symposium on Math. Stat. and Prob., Univ. of California Press, Berkeley, 1966, pp. 351–372.

    Google Scholar 

  6. H. Hermes, Calculus of set-valued functions and control,J. Math. Mech. 18 (1968), 47–60.

    Google Scholar 

  7. E. Hewitt andK. Stromberg,Real and Abstract Analysis, Springer-Verlag New York, Inc., New York, 1965.

    Google Scholar 

  8. C. J. Himmelberg, M. Q. Jacobs andF. S. Van Vleck, Measurable multifunctions, selectors, and Filippov's implicit functions lemma,J. Math. Anal. Appl. 25 (1969), 276–284.

    Google Scholar 

  9. C. J. Himmelberg andF. S. Van Vleck, Selection and implicit function theorems for multifunctions with Souslin graph,Bull. Acad. Polon. Sci., Sér. Sci. Math. Astron. Phys. 19 (1971), 911–916.

    Google Scholar 

  10. L. Hörmander, Sur la fonction d'appui des ensembles convexes dans un espace localement convexe,Ark. Mat. 3 (1954), 181–186.

    Google Scholar 

  11. M. Q. Jacobs, Remarks on some recent extensions of Filippov's implicit functions lemma,SIAM. J. Control 5 (1967), 622–627.

    Google Scholar 

  12. E. B. Lee andL. Markus,Foundations of Optimal Control Theory, John Wiley, New York, 1967.

    Google Scholar 

  13. L. Markus, The bang-bang principle, USAFOSR Scientific Report, Lecture Series in Differential Equations, Session 1, Control Theory (1965), pp. 25–45.

  14. E. Michael, Continuous selectors III,Ann. of Math. 65 (1957), 375–390.

    Google Scholar 

  15. E. Michael, Topologies on spaces of subsets,Trans. Amer. Math. Soc. 71 (1951), 152–182.

    Google Scholar 

  16. C. Olech, A note concerning set-valued measurable functions,Bull. Acad. Polon. Sci., Sér. Sci. Math. Astron. Phys. 13 (1965), 317–321.

    Google Scholar 

  17. C. Olech, Lexicographic order, range of integrals and “bang-bang” principle,Mathematical Theory of Control (A. V. Balakrishnan and L. W. Neustadt, eds.), Academic Press, New York, 1967, pp. 35–45.

    Google Scholar 

  18. R. Wegman, Der Wertebereich von Vektorintegralen,Z. Wahrscheinlichkeitstheorie Verw. Geb. 14 (1970), 203–238.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dauer, J.P., Van Vleck, F.S. Measurable selectors of multifunctions and applications. Math. Systems Theory 7, 367–376 (1973). https://doi.org/10.1007/BF01890613

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01890613

Keywords

Navigation