Let $f \in L^p(\Omega)$ and $\varepsilon >0$. Show that exist a ball $B_R \subset \mathbb{R}^n$ such that $\int_{\Omega \backslash B_R}|f|^p < \varepsilon$.
$f \in L^p(\Omega) \Rightarrow$ that exist a ball $B_R \subset \mathbb{R}^n$ that \int_{\Omega \backslash B_R}|f|^p < \varepsilon.
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analysis
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0Also, you should ask a question rather than state an exercise. – 2012-08-29
1 Answers
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Hint: $\int_\Omega = \sum_{n=1}^\infty \int_{\Omega \cap \{x: n-1 \le |x| < n\}}$