| Title:
|
Normal integrands and related classes of functions (English) |
| Author:
|
Kucia, Anna |
| Author:
|
Nowak, Andrzej |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
775-781 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $D\subset T\times X$, where $T$ is a measurable space, and $X$ a topological space. We study inclusions between three classes of extended real-valued functions on $D$ which are upper semicontinuous in $x$ and satisfy some measurability conditions. (English) |
| Keyword:
|
normal integrand |
| Keyword:
|
Carathéodory function |
| MSC:
|
28A20 |
| MSC:
|
28B20 |
| MSC:
|
54C30 |
| idZBL:
|
Zbl 0883.54022 |
| idMR:
|
MR1378698 |
| . |
| Date available:
|
2009-01-08T18:21:37Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118804 |
| . |
| Reference:
|
[1] Ash R.B.: Real Analysis and Probability.Academic Press, New York, 1972. MR 0435320 |
| Reference:
|
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| Reference:
|
[3] Burgess J., Maitra A.: Nonexistence of measurable optimal selections.Proc. Amer. Math. Soc. 116 (1992), 1101-1106. Zbl 0767.28010, MR 1120505 |
| Reference:
|
[4] Christensen J.P.R.: Topology and Borel Structure.North Holland, Amsterdam, 1974. Zbl 0273.28001, MR 0348724 |
| Reference:
|
[5] Himmelberg C.J.: Measurable relations.Fund. Math. 87 (1975), 53-72. Zbl 0296.28003, MR 0367142 |
| Reference:
|
[6] Kucia A.: Some counterexamples for Carathéodory functions and multifunctions.submitted to Fund. Math. |
| Reference:
|
[7] Kucia A., Nowak A.: On Baire approximations of normal integrands.Comment. Math. Univ. Carolinae 30:2 (1989), 373-376. Zbl 0685.28001, MR 1014136 |
| Reference:
|
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| Reference:
|
[9] Levin V.L.: Measurable selections of multivalued mappings into topological spaces and upper envelopes of Carathéodory integrands (in Russian).Dokl. Akad. Nauk SSSR 252 (1980), 535-539 English transl.: Sov. Math. Dokl. 21 (1980), 771-775. MR 0577834 |
| Reference:
|
[10] Levin V.L.: Convex Analysis in Spaces of Measurable Functions and its Applications to Mathematics and Economics (in Russian).Nauka, Moscow, 1985. MR 0809179 |
| Reference:
|
[11] Pappas G.S.: An approximation result for normal integrands and applications to relaxed controls theory.J. Math. Anal. Appl. 93 (1983), 132-141. Zbl 0521.49012, MR 0699706 |
| Reference:
|
[12] Rockafellar R.T.: Integral functionals, normal integrands and measurable selections.in: Nonlinear Operators and Calculus of Variations (L. Waelbroeck, ed.), Lecture Notes in Mathematics 543, Springer, Berlin, 1976, pp. 157-207. Zbl 0374.49001, MR 0512209 |
| Reference:
|
[13] Schäl M.: A selection theorem for optimization problem.Arch. Math. 25 (1974), 219-224. MR 0346632 |
| Reference:
|
[14] Wagner D.H.: Survey of measurable selection theorems.SIAM J. Control 15 (1977), 859-903. Zbl 0407.28006, MR 0486391 |
| Reference:
|
[15] Zygmunt W.: Scorza-Dragoni property (in Polish).UMCS, Lublin, 1990. |
| . |
