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

Authors

  • Charles Swartz New Mexico State University.

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-01-0008

Keywords:

Weak convergence, Weak compactness, Integrable functions, Measure and integration

Abstract

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.

References

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Published

2020-02-04

How to Cite

[1]
C. Swartz, “Weak convergence and weak compactness in the space of integrable functions with respect to a vector meansure”, Proyecciones (Antofagasta, On line), vol. 39, no. 1, pp. 123-133, Feb. 2020.

Issue

Section

Artículos