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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} +$$\| f + g \|_p \leq \|f\|_p + \|g\|_p$$ |