On Weak Compactness and Lower Closure Results for Pettis Integrable (Multi)Functions
Tom 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 53-61
MSC: Primary 28A20, 28B05.
DOI: 10.4064/ba52-1-6
Streszczenie
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.
