Measurability and integrability of the weak upper limit of a sequence of multifunctions

AbstractWe provide several properties of the weak upper limit of a sequence of subsets of a separable Banach space, such as a criterion of non-vacuity, of closedness, etc. We also examine the measurability of the multifunction defined as the weak upper limit of a sequence of multifunctions. At last, applications to the existence of a measurable and Bochner integrable selector for this multifunction are presented