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On Compactness in Spaces of Bochner Integrable Functions

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Abstract

We show that a bounded subset K of L p(μ,X) is relatively norm compact if and only if K is p-uniformly integrable, scalarly relatively compact, and either tight or flatly concentrated. The scalar relative compactness can be also replaced by several oscillation criteria.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada II Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain

    S. Diaz & F. Mayoral

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  1. S. Diaz
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  2. F. Mayoral
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Diaz, S., Mayoral, F. On Compactness in Spaces of Bochner Integrable Functions. Acta Mathematica Hungarica 83, 231–239 (1999). https://doi.org/10.1023/A:1006721122987

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