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On Carathéodory type selectors in a Hilbert space. (English) Zbl 0593.54018
Pr. Nauk Uniw. Śląsk. Katowicach 752, Ann. Math. Silesianae 2(14), 47-52 (1986).
Summary: We consider a set-valued function of two variables, measurable in the first and continuous in the second variable. Using metric projections we construct for this function a family of selectors which are Carathéodory maps. The existence of Carathéodory selectors was studied by Castaing, Cellina, Fryszkowski, and the first author.

MSC:
54C65 Selections in general topology
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
93B05 Controllability
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections