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In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence , does there exist a positive Borel measure μ on the real line such that
In other words, an affirmative answer to the problem means that is the sequence of moments of some positive Borel measure μ.
The Stieltjes moment problem, Vorobyev moment problem, and the Hausdorff moment problem are similar but replace the real line by {\displaystyle } , or a bounded interval.
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