Weak convergence and weak compactness in the space of integrable functions with respect to a vector meansure

• Swartz, Charles ^[1]
  1. [1] New Mexico State University

     New Mexico State University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 1, 2020, págs. 123-133
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-01-0008
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• Resumen

  • We consider weak convergence and weak compactness in the space L1(m) of real valued integrable functions with respect to a Banach space calued measure m equipped with its natural norm. We give necessary and sufficient conditions for a sequence in L1(m) to be weak Cauchy, and we give necessary and sufficient conditions for a subset of L1(m) to be conditionally sequentially weakly compact.

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