2011-8 Geometric Mean

Let f be a continuous function on [0,1]. Prove that \[ \lim_{n\to \infty}\int_0^1 \cdots \int_0^1 f(\sqrt[n]{x_1 x_2 \cdots x_n } ) dx_1 dx_2 \cdots dx_n = f(1/e).\]

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2 thoughts on “2011-8 Geometric Mean

  1. S. Oum Post author

    오른쪽 위에 적혀있습니다. 다시 적자면…

    Email your solution to sangil at kaist.edu, or bring it to Dept. of Math. Sci. and ask to put it into the mailbox of Prof. Sang-il Oum (엄상일).

    If you are emailing, please include “POW20##-#”(problem no) in the subject.

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