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According to Wikipedia, the $L_p$-norm is not subadditive when $p\in(0,1)$. How can I show that the map $n_p(f)=(\int_0^1|f(x)|^p~\mathrm{d}x)^{2p}$ is not subadditive for $f\in C[0,1]$ for $0?

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    Is the power of the integral purposely $2p$ or should it be $\frac{1}{p}$?2012-09-11

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