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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pointwise limits of Birkhoff integrable functions


Author: José Rodríguez
Journal: Proc. Amer. Math. Soc. 137 (2009), 235-245
MSC (2000): Primary 28B05, 46G10
Published electronically: August 13, 2008
MathSciNet review: 2439446
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Abstract: We study the Birkhoff integrability of pointwise limits of sequences of Birkhoff integrable Banach space-valued functions, as well as the convergence of the corresponding integrals. Both norm and weak convergence are considered. We discuss the roles that equi-Birkhoff integrability and the Bourgain property play in these problems. Incidentally, a convergence theorem for the Pettis integral with respect to the norm topology is presented.


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Additional Information

José Rodríguez
Affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Email: jorodrui@mat.upv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09589-0
PII: S 0002-9939(08)09589-0
Keywords: Birkhoff integral, Pettis integral, Bourgain property, pointwise limit, convergence theorem
Received by editor(s): January 8, 2008
Published electronically: August 13, 2008
Additional Notes: This research was supported by the Spanish grant MTM2005-08379 (MEC and FEDER)
Communicated by: Tatiana Toro
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.