Two theorems on the Scorza Dragoni property for multifunctions

Gabriele Bonanno

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1989)

  • Volume: 83, Issue: 1, page 51-56
  • ISSN: 1120-6330

Abstract

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We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.

How to cite

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Bonanno, Gabriele. "Two theorems on the Scorza Dragoni property for multifunctions." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 83.1 (1989): 51-56. <http://eudml.org/doc/287399>.

@article{Bonanno1989,
abstract = {We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.},
author = {Bonanno, Gabriele},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Multifunction; Scorza Dragoni property; Carathéodory selection; multifunctions},
language = {eng},
month = {12},
number = {1},
pages = {51-56},
publisher = {Accademia Nazionale dei Lincei},
title = {Two theorems on the Scorza Dragoni property for multifunctions},
url = {http://eudml.org/doc/287399},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Bonanno, Gabriele
TI - Two theorems on the Scorza Dragoni property for multifunctions
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 51
EP - 56
AB - We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.
LA - eng
KW - Multifunction; Scorza Dragoni property; Carathéodory selection; multifunctions
UR - http://eudml.org/doc/287399
ER -

References

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  1. ARTSTEIN, Z. and PRIKRY, K., 1987. Carathéodory selections and the Scorza Dragoni property. J. Math. Anal. Appl., 127: 540-547. Zbl0649.28011MR915076DOI10.1016/0022-247X(87)90128-4
  2. BOURBAKI, N., 1966. General Topology. Part I, Hermann. Zbl0145.19302
  3. CASTAING, C. and VALADIER, M., 1977. Convex analysis and measurable multifunctions. Springer-Verlag. Zbl0346.46038MR467310
  4. CELLINA, A., 1976. A selection theorem. Rend. Sem. Mat. Univ. Padova, 55: 143-149. Zbl0362.54010MR474192
  5. HIMMELBERG, C.J., 1973. Precompact contraction of metric uniformities, and the continuity of F ⁢ ( t , x ) . Rend. Sem. Mat. Univ. Padova, 50: 185-188. Zbl0285.28018MR355958
  6. HIMMELBERG, C.J., 1974. Correction to: Precompact contraction of metric uniformities, and the continuity of F ⁢ ( t , x ) . Rend. Sem. Mat. Univ. Padova, 51: 360. Zbl0298.28017MR372813
  7. HIMMELBERG, C.J. and VAN VLECK, F.S., 1976. An extension of Brunovsky's Scorza Dragoni type theorem for unbounded set-valued functions. Math. Slovaca, 26: 47-52. Zbl0328.28004MR430205
  8. MICHAEL, E., 1956. Continuous selection I. Ann. of Math., 63: 361-382. Zbl0071.15902MR77107
  9. RICCERI, B., 1982. Carathéodory's selections for multifunctions with non-separable range. Rend. Sem. Mat. Univ. Padova, 67: 185-190. Zbl0503.28003MR682711
  10. RICCERI, B., 1984. On multifunctions with convex graph. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 77: 64-70. Zbl0611.54011MR884937
  11. RICCERI, B. and VILLANI, A., 1982. Separability and Scorza-Dragoni's property. Matematiche, 37: 156-161. Zbl0581.28004MR791334
  12. ZYGMUNT, W., 1987. On the Scorza-Dragoni's type property of the real function semicontinuous in the second variable. Rend. Acc. Naz. delle Scienze (detta dei XL), 105: I, 53-63 Zbl0654.28006MR930858

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