Fatou lemma for the Pettis integral.
Publicacions Matemàtiques, Tome 42 (1998) no. 1, p. 67-79.
The purpose of this paper is to present Fatou type results for a sequence of Pettis integrable functions and multifunctions. We prove the non vacuity of the weak upper limit of a sequence of Pettis integrable functions taking their values in a locally convex space and we deduce a Fatou's lemma for a sequence of convex weak compact valued Pettis integrable multifunctions. We prove as well a Lebesgue theorem for a sequence of Pettis integrable multifunctions with values in the space of convex compact sets of a separable Banach space.
Source:
Zbl
Classification : 26E25, 28B20 
@article{PMATES_1998__42_1_41334,
     author = {Allal Amrani},
     title = {Fatou lemma for the {Pettis} integral.},
     journal = {Publicacions Matem\`atiques},
     pages = {67-79},
     volume = {42},
     number = {1},
     year = {1998},
     zbl = {an:0933.28005},
     language = {fr},
     url = {https://geodesic-test.mathdoc.fr/item/PMATES_1998__42_1_41334/}
}
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Allal Amrani. Fatou lemma for the Pettis integral.. Publicacions Matemàtiques, Tome 42 (1998) no. 1, p. 67-79. https://geodesic-test.mathdoc.fr/item/PMATES_1998__42_1_41334/