MEASURABILITY OF SET-VALUED FUNCTIONS

Abstract

In the paper to the definition of measurability of set-valued functions such a a-algebra is presented by which the well-known properties of the real functions will furtheron hold, e.g. Lusin's and Egorov's theorems. The first two theorems discuss the correlation of the various definitions of measurability applied in the mathematical literature. The difficulty of proof lies in the fact that the Q space does not inherit the properties of basic space Z, thus the image space of the examined functions is not a compact metric space.