For $x\in\mathbb{R}^n$, 且 $p$ is conjugate number of $q$ and vice versa. (i.e. $p,q>1$ s.t. ${1\over p}+{1\over q}=1$), 則
$$ \begin{align} \|x\|p=\sup{\|y\|_q=1}\{|\langle x,y\rangle |\} \end{align} $$
Assume $p\geq1$. Then for any $x,y\in\mathbb{R}^n$ we have
$$ \|x+y\|_p\leq\|x\|_p+\|y\|_p $$