Abstract
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in measure but not a.e. pointwise, uniformly but not pointwise convergent, and uniformly convergent but not in \(L^1\)-norm, are analyzed. These findings extend and complement a number of earlier results by several authors.
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Dedicated to Professor Bernal-González on the occasion of his 60th birthday.
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The authors have been partially supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127, Grant P08-FQM-03543, and by MICINN Grant PGC2018-098474-B-C21.
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Calderón-Moreno, M.C., Gerlach-Mena, P.J. & Prado-Bassas, J.A. Lineability and modes of convergence. RACSAM 114, 18 (2020). https://doi.org/10.1007/s13398-019-00743-z
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DOI: https://doi.org/10.1007/s13398-019-00743-z
Keywords
- Lineability
- Algebrability
- Uniform convergence
- Convergence in measure
- Pointwise convergence
- Convergence in \(L^1\)-norm