On Hausdorff’s moment problem in higher dimensions
نویسنده
چکیده
Denote by μn = ∫ x n1 1 . . . x nd d dμ(x) the n’th moment of a Borel probability measure μ on the unit cube I = [0, 1] in R. Generalizing results of Hausdorff, Hildebrandt and Schoenberg, we give a sufficient condition in terms of moments, that μ is absolutely continuous with respect to a second Borel measure ν on I. We also review a constructive approximation of measures by atomic measures using finitely many moments.
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