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On the integration of vector-valued functions

D. H. Fremlin·Jose Mendoza
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Abstract

We discuss relationships between the McShane, Pettis, Talagrand and Bochner integrals. A large number of different methods of integration of Banach-space-valued functions have been introduced, based on the various possible constructions of the Lebesgue integral. They commonly run fairly closely together when the range space is separable (or has w^*-separable dual) and diverge more or less sharply for general range spaces. The McShane integral as described by [Go] is derived from the `gauge-limit' integral of [McS]. Here we give both positive and negative results concerning it and the other three integrals listed above.

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D. H. Fremlin, Jose Mendoza. 1992-02-21. On the integration of vector-valued functions. https://arxiv.org/abs/math/9202202

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