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Convergence theorems for the Birkhoff integral

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Abstract

We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence (f n ) of functions from a measure space to a Banach space. In one result the equi-integrability of f n ’s is involved and we assume f n → f almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence of (f n ) to f is assumed.

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Authors and Affiliations

  1. Institute of Mathematicss, Technical University of Łódź, ul. Wólczańska 215, 90-924, Łódź, Poland

    Marek Balcerzak & Monika Potyrała

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  1. Marek Balcerzak
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  2. Monika Potyrała
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Correspondence to Marek Balcerzak.

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Balcerzak, M., Potyrała, M. Convergence theorems for the Birkhoff integral. Czech Math J 58, 1207–1219 (2008). https://doi.org/10.1007/s10587-008-0080-1

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  • DOI: https://doi.org/10.1007/s10587-008-0080-1

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