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Undominated Sequences of Integrable Functions

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Abstract

In this paper, we investigate to what extent the conclusion of the Lebesgue dominated convergence theorem holds if the assumption of dominance is dropped. Specifically, we study both topological and algebraic genericity of the family of all null sequences of functions that, being continuous on a locally compact space and integrable with respect to a given Borel measure in it, are not controlled by an integrable function.

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Acknowledgements

Luis Bernal-González, María del Carmen Calderón-Moreno, and José A. Prado-Bassas have been supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 Grant P08-FQM-03543 and by MCINN Grant PGC2018-098474-B-C21. Marina Murillo-Arcila is supported by MEC, Grant MTM2016-75963-P, and PID2019-105011GB-I00.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Instituto de Matemáticas Antonio de Castro Brzezicki (IMUS), Universidad de Sevilla, Avenida Reina Mercedes, 41012, Seville, Spain

    Luis Bernal-González, María del Carmen Calderón-Moreno & José A. Prado-Bassas

  2. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022, Valencia, Spain

    Marina Murillo-Arcila

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  1. Luis Bernal-González
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  2. María del Carmen Calderón-Moreno
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  3. Marina Murillo-Arcila
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  4. José A. Prado-Bassas
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Correspondence to Marina Murillo-Arcila.

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Bernal-González, L., del Carmen Calderón-Moreno, M., Murillo-Arcila, M. et al. Undominated Sequences of Integrable Functions. Mediterr. J. Math. 17, 179 (2020). https://doi.org/10.1007/s00009-020-01631-2

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  • DOI: https://doi.org/10.1007/s00009-020-01631-2

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