Pointwise compactness and continuity of the integral.

G. Vera

Revista Matemática de la Universidad Complutense de Madrid (1996)

  • Volume: 9, Issue: Extr., page 221-245
  • ISSN: 1139-1138

Abstract

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In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.

How to cite

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Vera, G.. "Pointwise compactness and continuity of the integral.." Revista Matemática de la Universidad Complutense de Madrid 9.Extr. (1996): 221-245. <http://eudml.org/doc/44214>.

@article{Vera1996,
abstract = {In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K. },
author = {Vera, G.},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Integrabilidad; Teoría de la medida; Medidas vectoriales; Desarrollo en serie de funciones; Compacidad; Espacios lineales topológicos; Convergencia puntual; Conjuntos de Baire; Metrizabilidad; Integrales de Pettis; continuity; canonical mapping; Banach spaces with the Pettis integral property; universal Pettis integrability},
language = {eng},
number = {Extr.},
pages = {221-245},
title = {Pointwise compactness and continuity of the integral.},
url = {http://eudml.org/doc/44214},
volume = {9},
year = {1996},
}

TY - JOUR
AU - Vera, G.
TI - Pointwise compactness and continuity of the integral.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1996
VL - 9
IS - Extr.
SP - 221
EP - 245
AB - In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.
LA - eng
KW - Integrabilidad; Teoría de la medida; Medidas vectoriales; Desarrollo en serie de funciones; Compacidad; Espacios lineales topológicos; Convergencia puntual; Conjuntos de Baire; Metrizabilidad; Integrales de Pettis; continuity; canonical mapping; Banach spaces with the Pettis integral property; universal Pettis integrability
UR - http://eudml.org/doc/44214
ER -

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