\begin{definition}[Definition:Measure of Finite Stieltjes Function]
Let $f: \R \to \R$ be a finite Stieltjes function.
Let $\mu_f$ be the pre-measure of $f$.
Let $\mu$ be the unique measure extending $\mu_f$ provided on Pre-Measure of Finite Stieltjes Function Extends to Unique Measure.
Then $\mu$ is called the '''measure of $f$'''.
This definition makes $\mu$ a measure on $\map \BB \R$, the Borel $\sigma$-algebra of $\R$.
\end{definition}