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.
@article{urn:eudml:doc:41334,
title = {Lemme de Fatou pour l'int\'egrale de Pettis.},
journal = {Publicacions Matem\`atiques},
volume = {42},
year = {1998},
pages = {67-79},
mrnumber = {MR1628138},
zbl = {0933.28005},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41334}
}
Amrani, Allal. Lemme de Fatou pour l'intégrale de Pettis.. Publicacions Matemàtiques, Tome 42 (1998) pp. 67-79. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41334/