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Published in:
2008 | OriginalPaper | Chapter
Tightness conditions and integrability of the sequential weak upper limit of a sequence of multifunctions
Authors : Charles Castaing, Christian Hess, Mohamed Saadoune
Published in: Advances in Mathematical Economics Volume 11
Publisher: Springer Japan
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Various notions of tightness for measurable multifunctions are introduced and compared. They are used to derive results on the existence of integrable selections for the sequential weak upper limit of a sequence of multifunctions. Similar questions are examined for multifunctions with values in a dual space. Some results are particularized in the single-valued case, and applications to the multidimensional Fatou Lemma, both in the primal and in the dual space, are derived. This is achieved under conditions weaker than or noncomparable to
L
1
-boundedness.