📂Lebesgue Spaces

Proof of Minkowski's Inequality in Lebesgue Spaces

Theorem[^1]

Let’s call $\Omega \subset \mathbb{R}^{n}$ an open set. If $1 \le p < \infty$ and $u, v \in L^{p}(\Omega)$, then

$$ \left\| u + v \right\|_{p} \le \left\| u \right\|_{p}+\left\| v \right\|_{p} $$

This is called the Minkowski inequality.