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arXiv · 2101.05887

On the set of G\^ateaux differentiability of the $L^1$ norm

Julio Delgado·Andrés F. Muñoz-Tello
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Abstract

Let $(\Omega, \mathcal{M}, \mu)$ be a measure space. In this paper we establish the set of G\^ateaux differentiability for the usual norm of $L^{1}(\Omega, \mu)$ and the corresponding derivative formulae at each point in this set.

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Julio Delgado, Andrés F. Muñoz-Tello. 2021-01-14. On the set of G\^ateaux differentiability of the $L^1$ norm. https://arxiv.org/abs/2101.05887

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