Pointwise limits of Birkhoff integrable functions

Rodríguez, José

doi:10.1090/S0002-9939-08-09589-0

Pointwise limits of Birkhoff integrable functions
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by José Rodríguez PDF

Proc. Amer. Math. Soc. 137 (2009), 235-245 Request permission

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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