p-adic measures with given Laurent moments (Q1089048)

Let f be a continuous function on \({\mathbb{Z}}_ p\). A necessary and sufficient condition for the existence of a measure \(\mu\) on \(1+p {\mathbb{Z}}_ p\) such that \(f(z)=\int \lambda^{-z} d\mu (\lambda)\) is given: from f a formal power series can be constructed whose coefficients have to be bounded. Such a result was already known. Proofs are elementary and complete.