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Trajectories of set valued integrals

Published online by Cambridge University Press:  17 April 2009

Nikolaos S. Papageorgiou
Nikolaos S. Papageorgiou
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, USA.
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Abstract

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The purpose of this paper is to study the trajectory multifunction Φ(·) determined by the indefinite set valued integral of a measurable Banach space valued multifunction F(·), that is for all t ∈ [0, T], , where the set valued integral is interpreted in the sense of Aumann. We study the topological and algebraic properties of SΦ equaling the set of selectors of Φ(·) whose primitive is an integrable selector of F(·). We also determine several useful properties that Φ(·) possesses and finally we present some convergence and stability results using the Kuratowski-Mosco convergence of sets.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 3 , June 1985 , pp. 389 - 411
Copyright
Copyright © Australian Mathematical Society 1985

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