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Math Help - limits and supremum norm

  1. #1
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    limits and supremum norm

    Show that lim(p-> infinity) ||x||p = ||x|| for all x in Rn
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  2. #2
    MHF Contributor

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    Here's a hint. Write (and justify) \left(\max_{1\leq i\leq n} |x_i|\right)^p\leq |x_1|^p+\cdots+|x_n|^p\leq n\left(\max_{1\leq i\leq n} |x_i|\right)^p. (Note: it would have been nice to know what you already tried to do in addition of just stating your question)
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