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

### Volume 83 / 2004

Annales Polonici Mathematici 83 (2004), 179-187
MSC: 47H04, 28B20, 34A60.
DOI: 10.4064/ap83-2-8

#### Abstract

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.