Idea Espacios de Lebesgue

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5 years 2 months ago #1556 by Diego_Chamorro
Replied by Diego_Chamorro on topic Espacios de Lebesgue
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5 years 2 months ago #1555 by Eduardo_Arias
Espacios de Lebesgue was created by Eduardo_Arias
Hola, tengo una duda.

En el ejercicio 4.4 de Espacios de Lebesgue, en la segunda parte:

¿Puedo decir lo siguiente?
\[\[ \left(\left\| f \right\|\right_{L^\infty})^r\geq \left\| \left| f \right|^r \right\|_{L^\infty}\]\]

Puesto que,
\[\[ \left\| \left| f \right|^r \right\|_{L^\infty}=\inf\{ c\in\bar{\mathbb{R}_+}\vert \mu(\{x\in X: |f(x)|>c^{1/r}\})=0 \} \] [\tex] y [tex] \[\left(\left\| f \right\|\right_{L^\infty})^r=\left( \inf=\{c\in\bar{\mathbb{R}_+}\vert \mu(\{x\in X: |f(x)|>c\})=0\} \right)^r\]\]

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