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

Download files

PDF

Citation rules

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

Similar Articles

Peter Raith, Topological transitivity for expanding monotonic mod one transformations with two monotonic pieces , Annales Mathematicae Silesianae: Vol. 13 (1999)
Tadeusz Pezda, Cycles of rational mappings in algebraically closed fields of positive characteristics , Annales Mathematicae Silesianae: Vol. 12 (1998)
Jozsef Bukor, Péter Filakovszky, János T. Tóth, On the diophantine equation x_1x_2···x_n = h(n)(x_1 + x_2 +...+ x_n) , Annales Mathematicae Silesianae: Vol. 12 (1998)
Sever S. Dragomir, Inequalities of Lipschitz type for power series in Banach algebras , Annales Mathematicae Silesianae: Vol. 29 (2015)
Iwona Krzemińska, A Cantor set in the intersection of sets of large measure , Annales Mathematicae Silesianae: Vol. 11 (1997)
Roman Ger, Justyna Sikorska, On the Cauchy equation on spheres , Annales Mathematicae Silesianae: Vol. 11 (1997)
Karol Baron, On the continuous dependence of solutions to orthogonal additivity problem on given functions , Annales Mathematicae Silesianae: Vol. 29 (2015)
Dariusz Dudzik, Marcin Skrzyński, Outer measures on a commutative ring induced by measures on its spectrum , Annales Mathematicae Silesianae: Vol. 31 (2017)
Bruce Ebanks, A Levi–Civita equation on monoids, two ways , Annales Mathematicae Silesianae: Vol. 36 No. 2 (2022)
Raghavendra G. Kulkarni, Insert a root to extract a root of quintic quickly , Annales Mathematicae Silesianae: Vol. 33 (2019)

<< < 4 5 6 7 8 9 10 11 12 13 > >>

You may also start an advanced similarity search for this article.

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

10.2478/amsil

Publisher

University of Silesia Press

Submit