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On the continuity of the integrable multifunctions

Piątek B.

Opuscula Mathematica

2009

Vol. 29, no. 1

81-88

The generalization of the Polovinkin theorem is studied.

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.

Remarks on set valued integrals of multifunctions with non empty bounded closed and convex values

Sambucini A.R.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

153-165

We study the comparison between the Aumann and the Bochner integrals for integrably non empty bounded closed convex valued multifunctions in a separable Banach space when it is not possible to apply embedding theoremes.