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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.
Amrani, Allal. "Lemme de Fatou pour l'intégrale de Pettis.." Publicacions Matemàtiques 42.1 (1998): 67-79. <http://eudml.org/doc/41334>.
@article{Amrani1998, author = {Amrani, Allal}, journal = {Publicacions Matemàtiques}, keywords = {Multifunción; Integrales de Pettis; Teoría del potencial; Pettis integrable functions; multifunctions; Fatou's lemma}, language = {fre}, number = {1}, pages = {67-79}, title = {Lemme de Fatou pour l'intégrale de Pettis.}, url = {http://eudml.org/doc/41334}, volume = {42}, year = {1998}, }
TY - JOUR AU - Amrani, Allal TI - Lemme de Fatou pour l'intégrale de Pettis. JO - Publicacions Matemàtiques PY - 1998 VL - 42 IS - 1 SP - 67 EP - 79 LA - fre KW - Multifunción; Integrales de Pettis; Teoría del potencial; Pettis integrable functions; multifunctions; Fatou's lemma UR - http://eudml.org/doc/41334 ER -