Add section on Minkowski's inequality in LP spaces

1 files changed, 5 insertions, 0 deletions

diff --git a/content/analysis_3.tex b/content/analysis_3.tex
index a288946..6ce2b80 100644
--- a/content/analysis_3.tex
+++ b/content/analysis_3.tex
@@ -568,3 +568,8 @@ Dann liegt für $f \in \L^p(\mu)$, $g \in \L^{p'}(\mu)$ das Produkt $fg \in \L^1
 $$\left| \int_X fg d\mu \right| \leq \int_X |fg| d\mu = \|fg\|_1 \leq \|f\|_p \|g\|_{p'}$$
 
 \subsection*{Minkowski Ungleichung}
+
+Seien $f, g \in \L^p(\mu)$. Dann gilt $f + g \in \L^p(\mu)$ und:
+
+\vspace{-2mm}
+$$\| f + g \|_p \leq \|f\|_p + \|g\|_p$$