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I'm stuck on the following problem :

Does there exist a real borel measure $\mu$ on $[0,1]$ such that

$$\int_{0}^{1}x^n d\mu = e^{-n^2}$$ for all $n \geq 1$ ?

Does anyone have any hint?

Thank you

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    Is $\mu$ supposed to be positive?2011-01-20
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    Hint: http://en.wikipedia.org/wiki/Hausdorff_moment_problem2011-01-20
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    Theo's link only seems to deal with the positive case. If you're interested in necessary and sufficient conditions in the general case, a good reference is chapter 3 of Widder's *The Laplace transform*. (Note that real finite measures correspond to functions of bounded variation, and Widder's exposition uses Stieltjes integrals.)2011-01-20

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