An Approach to the Ultrametric Moment Problem

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.