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...
| Authors: | , , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/92784 |
| Online Access: | https://hdl.handle.net/11441/92784 https://doi.org/10.1007/s13398-019-00743-z |
| Access Level: | Open access |
| Keyword: | Lineability Algebrability Uniform convergence Convergence in measure Pointwise convergence Convergence in L 1 -norm |
| 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 L1-norm, are analyzed. These findings extend and complement a number of earlier results by several authors. |
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