Minkowski inequality
= Minkowski inequality
{c}
{title2=$\|f+g\|_p\leq\|f\|_p+\|g\|_p$}
{wiki}
For $1\leq p\leq\infty$, the <Lp norm> satisfies the <triangle inequality>. For $1<p<\infty$, apply the <Holder inequality> to $\int(|f|+|g|)|f+g|^{p-1}$, then divide by $\|f+g\|_p^{p-1}$ when it is nonzero. The cases $p=1$ and $p=\infty$ follow directly from the pointwise triangle inequality. In particular, a series whose term norms have a finite sum converges in the complete $L^p$ space.