Kuratowski and Ryll-Nardzewski measurable selection theorem

Let X be a Polish space, \mathcal{B} (X) the Borel σ-algebra of X , (\Omega, \mathcal{F}) a measurable space and \psi a multifunction on \Omega taking values in the set of nonempty closed subsets of X . Suppose that \psi is \mathcal{F} -weakly measurable, that is, for every open subset U of X , we have :\{\omega : \psi (\omega) \cap U \neq \empty \} \in \mathcal{F}. Then \psi has a selection that is \mathcal{F} - \mathcal{B} (X) -measurable. == See also ==