Kuratowski Convergence for a Sequence of Random Sets

In this paper, we give equivalent definitions of the strong upper limit and the strong lower limit of a sequence of closed sets. According to the definitions, we prove the measurability of the strong upper limit and the strong lower limit and Lebesque’s dominated convergence theorems for the sequence of random sets. Analogous convergence results are also presented for the multivalued conditional expectations of these random sets.