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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Detalhes bibliográficos
Autores: Calderón Moreno, María del Carmen, Gerlach Mena, Pablo José, Prado Bassas, José Antonio
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/92784
Acesso em linha:https://hdl.handle.net/11441/92784
https://doi.org/10.1007/s13398-019-00743-z
Access Level:acceso abierto
Palavra-chave:Lineability
Algebrability
Uniform convergence
Convergence in measure
Pointwise convergence
Convergence in L 1 -norm
Descrição
Resumo: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.