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arXiv · 1807.09734

Algebraic structure of continuous, unbounded and integrable functions

M. Carmen Calderón-Moreno·Pablo J. Gerlach-Mena·José A. Prado-Bassas
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Abstract

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.

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M. Carmen Calderón-Moreno, Pablo J. Gerlach-Mena, José A. Prado-Bassas. 2018-07-25. Algebraic structure of continuous, unbounded and integrable functions. https://doi.org/10.1016/j.jmaa.2018.10.007

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