# Stieltjes Function of Measure of Finite Stieltjes Function

## Theorem

Let $f: \R \to \R$ be a finite Stieltjes function.

Let $\mu_f$ be the measure of $f$.

Let $f_{\mu_f}$ be the Stieltjes function of $\mu_f$.

Then $f_{\mu_f} = f$.