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authorAdrian Kummerlaender2017-03-18 21:41:01 +0100
committerAdrian Kummerlaender2017-03-18 21:41:01 +0100
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Add section on Minkowski's inequality in LP spaces
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diff --git a/content/analysis_3.tex b/content/analysis_3.tex
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@@ -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}
+$$\| f + g \|_p \leq \|f\|_p + \|g\|_p$$