In this note we associate to any compact $C$ 

in an ultrametric space $(X,d)$ a real valued 

and a $p$-adic valued measure $\mu _C$. 

We prove that any $p$-adic valued continuous 

function $f:C\rightarrow {\bf C}_p$ is $\mu _C$

-integrable. Using this measure we extend the 

definition of the trace function [2] to any 

$T\in {\bf C}_p$.