SciELO - Scientific Electronic Library Online

 
vol.39 issue1General solution and hyperstability results for a cubic radical functional equation related to quadratic mappingA cryptography method based on hyperbolicbalancing and Lucas-balancing functions author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google

Share


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

SWARTZ, Charles. Weak convergence and weak compactness in the space of integrable functions with respect to a vector measure. Proyecciones (Antofagasta) [online]. 2020, vol.39, n.1, pp.123-133. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-2020-01-0008.

We consider weak convergence and weak compactness in the space L1(m) of real valued integrable functions with respect to a Banach space valued 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.

Keywords : Weak convergence; Weak compactness; Integrable functions; Measure and integration.

        · text in English     · English ( pdf )