Document Type : Research Paper

Authors

• Julio Cesar Delgado Valencia ¹
• Andres Felipe Munoz-Tello ²

¹ Universidad del Valle, Departamento de Matematicas, Calle 13 100-00, Cali, Colombia

² Universidad Santiago de Cali, Calle 5 62-00, Cali, Colombia

Abstract

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

Keywords

• Gateaux differentiability
• Norms
• Measure