A New Version of the Multivalued Fatou Lemma

Abstract

H. Kudō introduced a notion of convergence of a sequence Bn of sub-σ-fields. We emphasize a connection with Mosco-convergence of associated subspaces L p E (Bn) where E is a separable Banach space with separable dual. This enables us to study the convergence of conditional expectation sequences of random sets and therefore to obtain a new version of the multivalued Fatou lemma.1991 Mathematics Subject Classification. 28B20.