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Pointwise Limits of Birkhoff Integrable Functions

José Rodríguez
Proceedings of the American Mathematical Society
Vol. 137, No. 1 (Jan., 2009), pp. 235-245
Stable URL: http://www.jstor.org/stable/20535729
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Pointwise Limits of Birkhoff Integrable Functions
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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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