Category:Definitions/Lp Norms

This category contains definitions related to Lp Norms.
Related results can be found in Category:Lp Norms.

We define the $L^p$ norm by:

$\ds \norm {\eqclass f \sim}_p = {\norm f}_p = \paren{ \int \size f^p \rd \mu }^{1/p}$

for each $\eqclass f \sim \in \map {L^p} {X, \Sigma, \mu}$, where $\norm \cdot_p$ is the $p$-seminorm.