Acta Mathematica

Borel selectors for upper semi-continuous set-valued maps

J. E. Jayne and C. A. Rogers

Full-text: Open access

Article information

Source
Acta Math. Volume 155 (1985), 41-79.

Dates
Received: 28 November 1983
Revised: 14 August 1984
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485890396

Digital Object Identifier
doi:10.1007/BF02392537

Mathematical Reviews number (MathSciNet)
MR793237

Zentralblatt MATH identifier
0588.54020

Rights
1985 © Almqvist & Wiksell

Citation

Jayne, J. E.; Rogers, C. A. Borel selectors for upper semi-continuous set-valued maps. Acta Math. 155 (1985), 41--79. doi:10.1007/BF02392537. https://projecteuclid.org/euclid.acta/1485890396


Export citation

References

  • Asplund, E., Fréchet differentiability of convex functions. Acta Math., 121 (1968), 31–47.
  • Asplund, E. & Rockafellar, R. T., Gradients of convex functions. Trans. Amer. Math. Soc., 139 (1969), 443–467.
  • Bessaga, C. & Peŀczynski, A., Selected topics in infinite-dimensional topology. Polish Sci. Publishers, Warsaw, 1975.
  • Bourgain, J., On dentability and the Bishop-Phelps property. Israel J. Math., 28 (1977), 265–271.
  • Brezis, H., Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Lecture Notes 5. North-Holland Publ. Co. Amsterdam, 1973.
  • Browder, F. E., Nonlinear operators and nonlinear equations of evolution in Banach spaces. Proc. Sympos. Pure Math., vol. 18, part 2, Amer. Math. Soc., Providence, R.I., 1976.
  • Davis, W. J. & Phelps, R. R., The Radon-Nikodým property and dentable sets in Banach spaces. Proc. Amer. Math. Soc., 45 (1974), 119–122.
  • Diestel, J., Geometry of Banach spaces-selected topics. Lecture Notes in Mathematics, 485, Springer-Verlag, New York, 1975.
  • Diestel, J. & Uhl, J. J., Vector measures, Math. Surveys no. 15, Amer. Math. Soc., Providence, R.I., 1977.
  • Edgar, G. A. & Wheeler, R. F., Topological properties of Banach spaces. Pacific J. Math., 115 (1984), 317–350.
  • Godefroy, G., Épluchabilité et unicité du prédual. Sem. Choquet, Comm. 11, 1977/78.
  • Hansell, R. W., Borel measurable mappings for nonseparable metric spaces. Trans. Amer. Math. Soc., 161 (1971), 145–169.
  • —, On Borel mappings and Baire functions. Trans. Amer. Math. Soc., 194 (1974), 195–211
  • Huff, F. E., Dentability and the Radon-Nikodým property. Duke Math. J., 41 (1974), 111–114.
  • James, R. C., Characterizations of reflexivity. Studia Math., 23 (1963/4), 205–216.
  • —, Weakly compact sets. Trans. Amer. Math. Soc., 113 (1964), 129–140.
  • —, A separable somewhat reflexive Banach space with non-separable dual. Bull. Amer. Math. Soc., 80 (1974), 738–743.
  • Jayne, J. E. & Rogers, C. A., Upper semi-continuous set-valued functions. Acta Math., 149 (1982), 87–125.
  • —, Borel selectors for upper semi-continuous multi-valued functions. J. Funct. Anal., 56 (1984), 279–299.
  • Kenderov, P. S., The set-valued monotone mappings are almost everywhere single-valued, C. R. Acad. Bulgare Sci., 27 (1974), 1173–1175.
  • —, Monotone operators in Asplund spaces. C. R. Acad. Bulgare Sci., 30 (1977), 963–964
  • —, Dense strong continuity of ponntwise continuous mappings. Pacific J. Math., 89 (1980), 111–130.
  • Kuratowski, K., Topology, vol. I. Academic Press, New York, 1966.
  • Maynard, H. B., A geometrical characterization of Banach spaces having the Radon-Nikodým property. Trans. Amer. Math. Soc., 185 (1973), 493–500.
  • Namioka, I. & Phelps, R. R., Banach spaces which are Asplund spaces. Duke Math. J., 42 (1975), 735–750.
  • Phelps, R. R., Dentability and extreme points in Banach spaces. J. Funct. Anal., 16 (1974), 78–90.
  • Phelps, R. R., Differentiability of convex functions on Banach spaces. Lecture Notes, University College London, 1978.
  • Rieffel, M. A., Dentable subsets of Banach spaces, with applications to a Radon-Nikodým theorem, in Functional Analysis (Proc. Conf., Irvine, Calif., 1966). B. R. Gelbaum, editor. Academic Press, pp. 71–77, 1967.
  • Robert, R., Une généralisation aux opérateurs monotones des théorèmes de différentiabilité d'Asplund. C. R. Acad. Sci. Paris Sér. A, 278 (1974), 1189–1191.
  • Rockafellar, R. T., Characterization of the subdifferentials of convex functions. Pacific J. Math., 17 (1966), 497–510.
  • —, Local boundedness of nonlinear monotone operators. Michigan Math. J., 16 (1969), 397–407.
  • —, On the maximal monotonicity of subdifferential mappings. Pacific J. Math., 33 (1970), 209–216.
  • Stegall, C., The Radon-Nikodým property in conjugate Banach spaces II. Trans. Amer. Math. Soc., 264 (1981), 507–519.
  • Bourgain, J. & Rosenthal, H., Geometrical implications of certain finite dimensional decompositions. Bull. Soc. Math. Belg., 32 (1980), 57–82.
  • Castaing, C. & Valadier, M., Convex analysis and measurable multifunctions. Lecture Notes in Mathematics, 580, Springer-Verlag, 1977.
  • Dulst, v. D. & Namioka, I., A note on trees in conjugate Banach spaces. Indag. Math., 46 (1984), 7–10.
  • Jayne, J. E. & Rogers, C. A., Sélections borélinennes de multi-applications semi-continues supérieurment. C. R. Acad. Sci. Paris Sér. I, 299 (1984), 125–128.
  • Kenderov, P. S., multivalued monotone mappings are almost everywhere single-valued. Studia Math., 56 (1976), 199–203.