Algebraic structure of continuous, unbounded and integrable functions

In this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in \([0,+\infty)\) and of the family of sequences of these functions converging to zero uniformly on compacta and in \(L^1\)-norm. In addition, we concentrate on the speed at whi...

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Bibliographic Details
Published in:arXiv.org 2018-09
Main Authors: Calderón-Moreno, M Carmen, Gerlach-Mena, Pablo J, Prado-Bassas, José A
Format: Article
Language:English
Subjects:
Algebra
Continuity (mathematics)
Convergence
Mathematical functions
Smoothness
Online Access:Get full text
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Summary:In this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in \([0,+\infty)\) and of the family of sequences of these functions converging to zero uniformly on compacta and in \(L^1\)-norm. In addition, we concentrate on the speed at which these functions grow, their smoothness and the strength of their convergence to zero.
ISSN:2331-8422
DOI:10.48550/arxiv.1807.09734