Lineability and modes of convergence

• 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
• ISSN: 1578-7303; 1579-1505
• DOI: 10.1007/s13398-019-00743-z

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.