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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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José Rodríguez
Affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

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.

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