Geodesic
An Approach to the Ultrametric Moment Problem
Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 251-256

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The classical Hausdorff–Widder–Bernstein theorem describes a 1–1 correspondence between probability measures $\mu$ on $[0,1]$ and a class of the so-called completely monotone functions $f$ on $(0,\infty)$ by means of the formula $f(x)=\int _0^1 s^x\,d\mu(s)$. In the present paper, we establish a non-Archimedean version of this theorem. 
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     author = {W. H. Schikhof},
     title = {An {Approach} to the {Ultrametric} {Moment} {Problem}},
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W. H. Schikhof. An Approach to the Ultrametric Moment Problem. Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 251-256. http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a24/