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On the fractional Pettis and Aumann-Pettis integral for multifunctions

Ibrahim A-G., Soliman A.M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 2

181-200

Let L 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.