Lemme de Fatou pour l'intégrale de Pettis

• Autores: Allal Amrani
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 42, Nº 1, 1998, págs. 67-79
• Idioma: francés
• Títulos paralelos:
  • Lema de Fatou para la integral de Pettis
  • Fatou lemma for the Pettis integral
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• Resumen

  • 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