On the integration of vector-valued functions

1992/02/21 by D. H. Fremlin, Fremlin, D. H., José Mendoza +1
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.math/9202202

openalex publication_date 1992/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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