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On the theory of Banach space valued multifunctions. II: Set valued martingales and set valued measures. (English) Zbl 0579.28010
This paper studies the convergence of set-valued martingales both in the Hausdorff metric and in the Kuratowski-Mosco sense. Then it proceeds and examines the measurability and integrability properties of the extreme points of multifunctions. Also the notion of weak convergence of multifunction is introduced, studied and compared with other modes of set convergence. This leads to a new convergence result for set-valued martingales. Finally set-valued measures are considered and an integral with respect to a set-valued measure is introduced and studied.

MSC:
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
46G10 Vector-valued measures and integration
60G48 Generalizations of martingales
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