In the present paper, we generalize, within the family of convex-valued multifunctions, a selection theorem of Cole (Ref. 1). This then leads us to prove some new results concerning Cesari's property (Q) and to the introduction of the Cesari limit of sets, which is then compared to the Kuratowski-Mosco limit.
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This work was done while the author was a visiting professor at the University of Pavia, Pavia, Italy. Financial support was provided by CNR and by NSF Grant No. 84-03135.
Communicated by L. Cesari
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Papageorgiou, N.S. On Cesari's property (Q). J Optim Theory Appl 53, 259–268 (1987). https://doi.org/10.1007/BF00939218
- selection theorems
- weak compactness
- Cesari's property (Q)
- Eberlein-Smulian theorem
- Cesari limit
- Kuratowski-Mosco limit
- Pettis measurability theorem