On Weak Compactness and Lower Closure Results for Pettis Integrable (Multi)Functions

Volume 52 / 2004

Erik J. Balder, Anna Rita Sambucini Bulletin Polish Acad. Sci. Math. 52 (2004), 53-61 MSC: Primary 28A20, 28B05. DOI: 10.4064/ba52-1-6


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.


  • Erik J. BalderMathematical Institute
    University of Utrecht
    Budapestlaan 6
    P.O. Box 80.010
    3508 TA Utrecht
    The Netherlands
  • Anna Rita SambuciniDepartment of Mathematics
    and Informatics
    University of Perugia
    Via L. Vanvitelli 1
    06100 Perugia, Italy

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