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Pointwise Limits of Birkhoff Integrable Functions
Proceedings of the American Mathematical Society
Vol. 137, No. 1 (Jan., 2009), pp. 235-245
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/20535729
Page Count: 11
You can always find the topics here!Topics: Mathematical integrals, Integrable functions, Topological theorems, Mathematical functions, Perceptron convergence procedure, Banach space, Mathematical theorems, Topology, Mathematical vectors
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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.
Proceedings of the American Mathematical Society © 2009 American Mathematical Society