\begin{definition}[Definition:P-Seminorm]
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Let $p \in \R$, $p \ge 1$.
Let $\map {\LL^p} \mu$ be Lebesgue $p$-space for $\mu$.
The '''$p$-seminorm''' on $\map {\LL^p} \mu$ is the mapping $\norm \cdot_p : \map {\LL^p} \mu \to \R_{\ge 0}$ defined by:
:$\ds \forall f \in \map {\LL^p} \mu: \norm f_p := \paren {\int \size f^p \rd \mu}^{1/p}$
That the '''$p$-seminorm''' is in fact a seminorm is proved on $p$-Seminorm is Seminorm.
\end{definition}