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On the integration of vector-valued functions

Fremlin, DH and Mendoza, J (1994) 'On the integration of vector-valued functions.' Illinois Journal of Mathematics, 38 (1). pp. 127-147. ISSN 0019-2082

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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.

Item Type: Article
Uncontrolled Keywords: math.FA
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 22 Apr 2021 14:59
Last Modified: 18 Aug 2022 12:47
URI: http://repository.essex.ac.uk/id/eprint/21545

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