Geodesic
On Weak Compactness and Lower Closure Results for Pettis Integrable (Multi)Functions
Erik J. Balder1 ; Anna Rita Sambucini2
1 Mathematical Institute University of Utrecht Budapestlaan 6 P.O. Box 80.010 3508 TA Utrecht The Netherlands
2 Department of Mathematics and Informatics University of Perugia Via L. Vanvitelli 1 06100 Perugia, Italy
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 53-61.

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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 Komlós theorem, which applies to scalarly integrable functions. Here it is shown that this same approach also applies to Pettis integrable multifunctions, because the abstract Komlós theorem can easily be extended so as to apply to generalized Pettis integrable functions. Some results in the literature are thus unified.
DOI : 10.4064/ba52-1-6
Keywords: abstract versatile approach given sequential weak compactness lower closure results scalarly integrable functions multifunctions its main tool abstract version koml theorem which applies scalarly integrable functions here shown approach applies pettis integrable multifunctions because abstract koml theorem easily extended apply generalized pettis integrable functions results literature unified

Erik J. Balder 1 ; Anna Rita Sambucini 2

1 Mathematical Institute University of Utrecht Budapestlaan 6 P.O. Box 80.010 3508 TA Utrecht The Netherlands
2 Department of Mathematics and Informatics University of Perugia Via L. Vanvitelli 1 06100 Perugia, Italy 
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Erik J. Balder; Anna Rita Sambucini. On Weak Compactness and Lower Closure Results
 for Pettis Integrable (Multi)Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 53-61. doi : 10.4064/ba52-1-6. http://geodesic.mathdoc.fr/articles/10.4064/ba52-1-6/

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