Let fbe continuous and non-negative on [a,b]. Show that $\displaystyle (\int_{a}^{b} f^{p})^{1/p} \rightarrowsup f(x) $ as $\displaystyle p\rightarrow\infty$
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You mean $\displaystyle (\int_{a}^{b} f^{p})^{1/p} \rightarrow \underset{a \leq x \leq b}{\mbox{sup}} f(x)$. What did you try? Do you have an idea why it's true?
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