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A generalization of the Bochner integral to locally convex spaces

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Abstract

We present a generalization of the Bochner integral to locally convex spaces. This generalization preserves the nuclearity of the mapping of the space of continuous functions on a compactum represented by the Bochner integral. We introduce locally convex spaces in which the study of a broad class of vector measures with values in these spaces reduces to the study of measures with values in a normed space. The results obtained are used to describe Fréchet spaces possessing the RN property.

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Authors and Affiliations

  1. Tula State Pedagogical Institute, USSR

    V. I. Rybakov

Authors
  1. V. I. Rybakov
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Translated from Matematicheskie Zametki, Vol. 18, No. 4, pp. 577–588, October, 1975.

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Rybakov, V.I. A generalization of the Bochner integral to locally convex spaces. Mathematical Notes of the Academy of Sciences of the USSR 18, 933–938 (1975). https://doi.org/10.1007/BF01153047

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  • DOI: https://doi.org/10.1007/BF01153047

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