DOI: 10.68381/jca19036 ISSN: 0944-6532
On Some Properties of Pettis Integrable Multifunctions
Nanda Dulal Chakraborty, Tanusree Choudhury
We study Aumann-Pettis integrable multifunctions on
2^X
2
X
, where X is a separable Banach space and their integrals. We prove the existence of a weakly compact convex-valued Pettis integrable multifunction F for a closed, convex, decomposable and weakly sequentially compact subset K of
P_1(\mu, X)
P
1
(
μ
,
X
)
, the space of all Pettis integrable functions on X such that K coincides with
S_F^P
S
F
P
, the collection of all Pettis integrable selectors of F. We also study the weak compactness property of
S_F^P
S
F
P
.