zbMATH — the first resource for mathematics

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.

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