Characterization of Carathéodory functions

Andrzej Nowak

Published: 2013-09-30

Vol. 27 (2013)

Characterization of Carathéodory functions

Andrzej Nowak

Abstract

We study Carathéodory functions f: D→Y , where (T, ????) is a measurable space, X, Y are metric spaces and D ⊂ T×X. In the case when ???? is complete and Y is a separable Banach space, we give a characterization of such functions.

Keywords:

Carathéodory function , extension , measurable selection

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Nowak, A. (2013). Characterization of Carathéodory functions. Annales Mathematicae Silesianae, 27, 93–98. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14006

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References

1. Appell J., Väth M., The space of Carathéodory functions , in: Nonlinear analysis and related problems, Tr. Inst. Mat. (Minsk) 2 Natl. Acad. Nauk Belarusi, Inst. Mat., Minsk, 1999, pp. 39–43 (in Russian).
2. Brown L., Schreiber B.M., Approximation and extension of random functions, Monatsh. Math. 107 (1989), 111–123.
3. Christensen J.P.R., Topology and Borel Structures, North Holland, Amsterdam, 1974.
4. DeBlasi F.S., Myjak J., On the random Dugundji extension theorem, J. Math. Anal. Appl. 128 (1987), 305–311.
5. Himmelberg C.J., Measurable relations, Fund. Math. 87 (1975), 53–72.
6. Kechris A.S., Classical Descriptive Set Theory, Springer-Verlag, New York, 1994.
7. Kucia A., Extending Carathéodory functions, Bull. Polish Acad. Sci. Math. 36 (1988), 593–601.
8. Kucia A., Some results on Carathéodory selections and extensions, J. Math. Anal. Appl. 223 (1998), 302–318.
9. Kuratowski K., Topology, Vol. II, Academic Press, New York, 1968.
10. Wagner D.H., Survey of measurable selection theorems, SIAM J. Control 15 (1977), 859–903.
11. Wagner D.H., Survey of measurable selection theorems: an update , in: Measure Theory, Oberwolfach 1979, Lecture Notes in Math., 794, Springer, Berlin–New York, 1980, pp. 176–219. Google Scholar

Vol. 27 (2013)
Published: 2013-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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