Lineability and modes of convergence

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 conv...

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Bibliographic Details
Published in:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 114; no. 1
Main Authors:	Calderón-Moreno, M. C., Gerlach-Mena, P. J., Prado-Bassas, J. A.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 2020 Springer Nature B.V
Subjects:	Algebra Applications of Mathematics Convergence Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theoretical Uniform convergence Lineability Secondary 15A03 Convergence in Primary 28A20 40A05 Convergence in measure Pointwise convergence Algebrability norm
Online Access:	Get full text
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Summary:	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.
ISSN:	1578-7303 1579-1505
DOI:	10.1007/s13398-019-00743-z