Lineability and modes of convergence
|Author||Calderón Moreno, María del Carmen
Gerlach Mena, Pablo José
Prado Bassas, José Antonio
|Department||Universidad de Sevilla. Departamento de Análisis Matemático|
|Published in||Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 114 (18)|
|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 ...
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 L1-norm, are analyzed. These findings extend and complement a number of earlier results by several authors.
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