Lineability and modes of convergence
Functional Analysis
2019-12-19 v1 Classical Analysis and ODEs
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 convergent in measure but not a.e.~pointwise, uniformly but not pointwise convergent, and uniformly convergent but not in -norm, are analyzed. These findings extend and complement a number of earlier results by several authors.
Cite
@article{arxiv.1907.02103,
title = {Lineability and modes of convergence},
author = {M. Carmen Calderón-Moreno and Pablo J. Gerlach-Mena and José A. Prado-Bassas},
journal= {arXiv preprint arXiv:1907.02103},
year = {2019}
}