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Some remarks on measurable and semi-continuous multifunctions

Liftings, Multifunctions And Selections

Part of the Lecture Notes in Mathematics book series (LNM,volume 1089)

Abstract

In this paper we extend some earlier results on measurable and semi-continuous multifunctions and give some examples to indicate the sharpness of certain theorems.

Keywords

  • Topological Space
  • Polish Space
  • Weak Measurability
  • Converse Inclusion
  • Baire Class

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Supported by the South African Council for Scientific and Industrial Research.

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References

  1. C. Castaing, Sur les multi-applications measurables, Rev. Francaise Informat. Recherche Opérationnelle 1, (1967), pp. 91–126.

    MathSciNet  MATH  Google Scholar 

  2. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg, 1975.

    MATH  Google Scholar 

  3. J.D. Dauer and F.S. van Vleck, Measurable selectors of multifunctions and applications, Math. Systems Theory, 7 (1974), pp. 367–376.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. G. Debreu, Integration of Correspondences, Proc. Fifth Berkeley Symp. Math. Statist. and Probability (1965/66), vol. II, Univ. of California Press, Berkeley, CA, 1967, pp. 351–372.

    Google Scholar 

  5. C.J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), pp. 53–72.

    MathSciNet  MATH  Google Scholar 

  6. C.J. Himmelberg, T. Parthasarathy and F.S. van Vleck, On measurable relations, Fund. Math. 111 (1981), pp. 161–167.

    MathSciNet  MATH  Google Scholar 

  7. K. Kuratowski, Topology, Volume II, Academic Press, 1968.

    Google Scholar 

  8. —, Some problems concerning semi-continuous set-valued mappings, Lecture Notes in Mathematics 171, Springer-Verlag, 1970, pp. 45–48.

    Google Scholar 

  9. P. Maritz, Integration of set-valued functions, Thesis, Leiden, 1975.

    Google Scholar 

  10. —, On a projection theorem for multifunctions, To appear in Quaestiones Mathematicae.

    Google Scholar 

  11. E. Michael, Topologies on Spaces of Subsets, Trans, Amer. Math. Soc. 71 (1951), pp. 152–182.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. T. Nishiura, Two counterexamples for measurable relations, Rocky Mountain J. of Math. 9 (1979), pp. 499–501.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. D. Wagner, Survey of measurable selection theorems, SIAM J. Control and Optimization 15 (1977), pp. 859–903.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1984 Springer-Verlag

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Maritz, P. (1984). Some remarks on measurable and semi-continuous multifunctions. In: Kölzow, D., Maharam-Stone, D. (eds) Measure Theory Oberwolfach 1983. Lecture Notes in Mathematics, vol 1089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072607

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  • DOI: https://doi.org/10.1007/BFb0072607

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13874-7

  • Online ISBN: 978-3-540-39069-5

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