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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.1 Antofagasta Feb. 2020 


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

Charles Swartz1 

1 New Mexico State University, Mathematics Dept, Las Cruces, NM, U. S. A. E-mail:


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

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The author would like to thank Susumu Okada for his help.


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Received: December 2018; Accepted: August 2019

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