Measure of Stieltjes Function of Measure

Theorem
Let $\mu$ be a measure on $\mathcal B \left({\R}\right)$, the Borel $\sigma$-algebra on $\R$.

Suppose that for all $n \in \N$, $\mu$ satisfies:


 * $\mu \left({ \left[{-n \,.\,.\, n}\right) \ }\right) < +\infty$

Let $f_\mu$ be the Stieltjes function of $\mu$.

Let $\mu_{f_\mu}$ be the measure of $f_\mu$.

Then $\mu_{f_\mu} = \mu$.