Paper's Title:

The ε-Small Ball Drop Property

Author(s):

C. Donnini and A. Martellotti

Dipartimento di Statistica e Matematica per la Ricerca Economica,
Universitą degli Studi di Napoli "Parthenope",
Via Medina, 80133 Napoli,
Italy
chiara.donnini@uniarthenope.it

{Dipartimento di Matematica e Informatica,
Universitą degli Studi di Perugia,
Via Pascoli - 06123 Perugia,
Italy.
amart@dipmat.unipg.it
URL: www.dipmat.unipg.it/~amart/

Abstract:

We continue the investigation on classes of small sets in a Banach space that give alternative formulations of the Drop Property. The small sets here considered are the set having the small ball property, and we show that for sets having non-empty intrinsic core and whose affine hull contains a closed affine space of infinite dimension the Drop Property can be equivalently formulated in terms of the small ball property.

Paper's Title:

A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral

Author(s):

Domenico Candeloro¹, Anca Croitoru², Alina Gavriluţ², Anna Rita Sambucini¹

¹Dept. of Mathematics and Computer Sciences,
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
Italy.
E-mail:  domenico.candeloro@unipg.it, anna.sambucini@unipg.it

²Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
E-mail: croitoru@uaic.ro, gavrilut@uaic.ro

Abstract:

In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.

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