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

Abstract 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 necessa...

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Autor principal:	Swartz,Charles
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Weak convergence Weak compactness Integrable functions Measure and integration
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000100123
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spelling	oai:scielo:S0716-091720200001001232020-02-18Weak convergence and weak compactness in the space of integrable functions with respect to a vector measureSwartz,Charles 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 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.1 20202020-02-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000100123en10.22199/issn.0717-6279-2020-01-0008
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Weak convergence Weak compactness Integrable functions Measure and integration
spellingShingle	Weak convergence Weak compactness Integrable functions Measure and integration Swartz,Charles Weak convergence and weak compactness in the space of integrable functions with respect to a vector measure
description	Abstract 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.
author	Swartz,Charles
author_facet	Swartz,Charles
author_sort	Swartz,Charles
title	Weak convergence and weak compactness in the space of integrable functions with respect to a vector measure
title_short	Weak convergence and weak compactness in the space of integrable functions with respect to a vector measure
title_full	Weak convergence and weak compactness in the space of integrable functions with respect to a vector measure
title_fullStr	Weak convergence and weak compactness in the space of integrable functions with respect to a vector measure
title_full_unstemmed	Weak convergence and weak compactness in the space of integrable functions with respect to a vector measure
title_sort	weak convergence and weak compactness in the space of integrable functions with respect to a vector measure
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000100123
work_keys_str_mv	AT swartzcharles weakconvergenceandweakcompactnessinthespaceofintegrablefunctionswithrespecttoavectormeasure
_version_	1718439864865652736

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

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