Normal integrands and related classes of functions
Kucia, Anna ; Nowak, Andrzej
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 775-781 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1995-01-01
Classification:  28A20,  28B20,  54C30 
@article{118804,
     author = {Anna Kucia and Andrzej Nowak},
     title = {Normal integrands and related classes of functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {775-781},
     zbl = {0883.54022},
     mrnumber = {1378698},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118804}
}

Kucia, Anna; Nowak, Andrzej. Normal integrands and related classes of functions. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 775-781. http://gdmltest.u-ga.fr/item/118804/

Ash R.B. Real Analysis and Probability, Academic Press, New York, 1972. | MR 0435320

Berliocchi H.; Lasry J.-M. Intégrandes normales et mesures paramétrées en calcul de variations, Bull. Soc. Math. France 101 (1973), 129-184. (1973) | MR 0344980

Burgess J.; Maitra A. Nonexistence of measurable optimal selections, Proc. Amer. Math. Soc. 116 (1992), 1101-1106. (1992) | MR 1120505 | Zbl 0767.28010

Christensen J.P.R. Topology and Borel Structure, North Holland, Amsterdam, 1974. | MR 0348724 | Zbl 0273.28001

Himmelberg C.J. Measurable relations, Fund. Math. 87 (1975), 53-72. (1975) | MR 0367142 | Zbl 0296.28003

Kucia A. Some counterexamples for Carathéodory functions and multifunctions, submitted to Fund. Math.

Kucia A.; Nowak A. On Baire approximations of normal integrands, Comment. Math. Univ. Carolinae 30:2 (1989), 373-376. (1989) | MR 1014136 | Zbl 0685.28001

Kucia A.; Nowak A. Relations among some classes of functions in mathematical programming, Mat. Metody Sots. Nauk 22 (1989), 29-33. (1989) | MR 1111399 | Zbl 0742.49009

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. (1980) | MR 0577834

Levin V.L. Convex Analysis in Spaces of Measurable Functions and its Applications to Mathematics and Economics (in Russian), Nauka, Moscow, 1985. | MR 0809179

Pappas G.S. An approximation result for normal integrands and applications to relaxed controls theory, J. Math. Anal. Appl. 93 (1983), 132-141. (1983) | MR 0699706 | Zbl 0521.49012

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. | MR 0512209 | Zbl 0374.49001

Schäl M. A selection theorem for optimization problem, Arch. Math. 25 (1974), 219-224. (1974) | MR 0346632

Wagner D.H. Survey of measurable selection theorems, SIAM J. Control 15 (1977), 859-903. (1977) | MR 0486391 | Zbl 0407.28006

Zygmunt W. Scorza-Dragoni property (in Polish), UMCS, Lublin, 1990.