Definition ($L^{p}$ norm)

Let $L^{p}$ be the Lp Space for some $1\le p<\infty$. We then define the $L^p$ norm on $L^{p}(X,\mathcal{F},\mu)$ as follows: $$\|f\|_{L^{p}}=\left( \int\limits _{X}|f|^{p} \, d\mu \right)^{\frac{1}{p}}$$