# Stieltjes Integrals Considered as Lengths

• Karl Menger
Chapter

## Abstract

The Stieltjes integral
$$\begin{array}{*{20}{c}} {\int\limits_{a}^{b} {f(x)dg(x)} } & {or briefly, \int\limits_{a}^{b} {fdg} }\\\end{array}$$
is defined as follows: We divide the interval [a, b] into a finite number of intervals
$$a = {{x}_{0}} < {{x}_{1}} <\ldots< {{x}_{{n - 1}}} < {{x}_{n}} = b.$$