In [4, 5, 7] an abstract, versatile approach was given to sequential weak compactness and lower closure results for scalarly integrable functions and multifunctions. Its main tool is an abstract version of the Komlos theorem, which applies to scalarly integrable functions. Here it is shown that this same approach also applies to Pettis integrable multifunctions, because the abstract Komlos theorem can easily be extended so as to apply to generalized Pettis integrable functions. Some results in the literature are thus unified.
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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.
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