Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions

Giovanni Anello¹ ; Paolo Cubiotti¹

¹ Department of Mathematics University of Messina Contrada Papardo, Salita Sperone 31 98166 Messina, Italy

Annales Polonici Mathematici, Tome 83 (2004) no. 2, pp. 179-187.

Résumé

We consider a multifunction $F:T\times X\to 2^E$, where $T$, $X$ and $E$ are separable metric spaces, with $E$ complete. Assuming that $F$ is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for $F$ which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.

Détail

DOI : 10.4064/ap83-2-8

Keywords: consider multifunction times where separable metric spaces complete assuming jointly measurable product lower semicontinuous second variable establish existence selection which measurable respect first variable continuous respect second result spirit where multifunctions only variable considered