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.
Segnalo due teoremi sulla proprietà di Scorza Dragoni per le multifunzioni. Come applicazione, in particolare, miglioro un teorema di A. Cellina [4] sulle selezioni di Carathéodory, rimuovendo un'ipotesi di compattezza.
@article{RLINA_1989_8_83_1_51_0,
author = {Gabriele Bonanno},
title = {Two theorems on the Scorza Dragoni property for multifunctions},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
volume = {83},
year = {1989},
pages = {51-56},
zbl = {0768.28002},
mrnumber = {1142437},
language = {en},
url = {http://dml.mathdoc.fr/item/RLINA_1989_8_83_1_51_0}
}
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, Tome 83 (1989) pp. 51-56. http://gdmltest.u-ga.fr/item/RLINA_1989_8_83_1_51_0/
[1] and , 1987. Carathéodory selections and the Scorza Dragoni property. J. Math. Anal. Appl., 127: 540-547. | MR 915076 | Zbl 0649.28011
[2] , 1966. General Topology. Part I, Hermann. | Zbl 0145.19302
[3] and , 1977. Convex analysis and measurable multifunctions. Springer-Verlag. | MR 467310 | Zbl 0346.46038
[4] , 1976. A selection theorem. Rend. Sem. Mat. Univ. Padova, 55: 143-149. | MR 474192 | Zbl 0362.54010
[5] , 1973. Precompact contraction of metric uniformities, and the continuity of . Rend. Sem. Mat. Univ. Padova, 50: 185-188. | MR 355958 | Zbl 0285.28018
[6] , 1974. Correction to: Precompact contraction of metric uniformities, and the continuity of . Rend. Sem. Mat. Univ. Padova, 51: 360. | MR 355958 | Zbl 0285.28018
[7] and , 1976. An extension of Brunovsky's Scorza Dragoni type theorem for unbounded set-valued functions. Math. Slovaca, 26: 47-52. | MR 430205 | Zbl 0328.28004
[8] , 1956. Continuous selection I. Ann. of Math., 63: 361-382. | MR 77107 | Zbl 0071.15902
[9] , 1982. Carathéodory's selections for multifunctions with non-separable range. Rend. Sem. Mat. Univ. Padova, 67: 185-190. | MR 682711 | Zbl 0503.28003
[10] , 1984. On multifunctions with convex graph. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 77: 64-70. | MR 884937 | Zbl 0611.54011
[11] and , 1982. Separability and Scorza-Dragoni's property. Matematiche, 37: 156-161. | MR 791334 | Zbl 0581.28004
[12] , 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 | MR 930858 | Zbl 0654.28006