Definition:Measure of Finite Stieltjes Function

Definition
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 $\mathcal B \left({\R}\right)$, the Borel $\sigma$-algebra of $\R$.

Also see

 * Pre-Measure of Finite Stieltjes Function
 * Pre-Measure of Finite Stieltjes Function Extends to Unique Measure
 * Stieltjes Function of Measure on Real Numbers