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On the Fractional Pettis and Aumann-Pettis Integral for Multifunctions

Ahmed-G. IbrahimAsmaa M. Soliman — 2006

Commentationes Mathematicae

Let α be a positive real number. In the present paper we present the definition of the Aumann Pettis integral and the Pettis integral of order α 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 α and for multifunctions.

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