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Let be a positive real number. In the present paper we present the definition of the Aumann Pettis integral and the Pettis integral of order for multifunctions. The properties of these integrals and the relations between them are studied extensively. In particular, a Strassen type theorem in this case and continuation property are proved. Also, we give a version for Fatou’s lemma and dominated convergence theorem for the Aumann-Pettis integral of order and for multifunctions.
We prove an existence theorem of solutions for a nonconvex sweeping process with nonconvex noncompact perturbation in Hilbert space. We do not assume that the values of the orient field are compact.
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