Normal integrands and related classes of functions

Anna Kucia; Andrzej Nowak

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 4, page 775-781
  • ISSN: 0010-2628

Abstract

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Let D ⊂ T × 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.

How to cite

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Kucia, Anna, and Nowak, Andrzej. "Normal integrands and related classes of functions." Commentationes Mathematicae Universitatis Carolinae 36.4 (1995): 775-781. <http://eudml.org/doc/247759>.

@article{Kucia1995,
abstract = {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.},
author = {Kucia, Anna, Nowak, Andrzej},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {normal integrand; Carathéodory function; normal integrand; Carathéodory function},
language = {eng},
number = {4},
pages = {775-781},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Normal integrands and related classes of functions},
url = {http://eudml.org/doc/247759},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Kucia, Anna
AU - Nowak, Andrzej
TI - Normal integrands and related classes of functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 4
SP - 775
EP - 781
AB - 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.
LA - eng
KW - normal integrand; Carathéodory function; normal integrand; Carathéodory function
UR - http://eudml.org/doc/247759
ER -

References

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  2. Berliocchi H., Lasry J.-M., Intégrandes normales et mesures paramétrées en calcul de variations, Bull. Soc. Math. France 101 (1973), 129-184. (1973) MR0344980
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  7. Kucia A., Nowak A., On Baire approximations of normal integrands, Comment. Math. Univ. Carolinae 30:2 (1989), 373-376. (1989) Zbl0685.28001MR1014136
  8. Kucia A., Nowak A., Relations among some classes of functions in mathematical programming, Mat. Metody Sots. Nauk 22 (1989), 29-33. (1989) Zbl0742.49009MR1111399
  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. (1980) MR0577834
  10. Levin V.L., Convex Analysis in Spaces of Measurable Functions and its Applications to Mathematics and Economics (in Russian), Nauka, Moscow, 1985. MR0809179
  11. Pappas G.S., An approximation result for normal integrands and applications to relaxed controls theory, J. Math. Anal. Appl. 93 (1983), 132-141. (1983) Zbl0521.49012MR0699706
  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. Zbl0374.49001MR0512209
  13. Schäl M., A selection theorem for optimization problem, Arch. Math. 25 (1974), 219-224. (1974) MR0346632
  14. Wagner D.H., Survey of measurable selection theorems, SIAM J. Control 15 (1977), 859-903. (1977) Zbl0407.28006MR0486391
  15. Zygmunt W., Scorza-Dragoni property (in Polish), UMCS, Lublin, 1990. 

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