Talk:Riemann-Stieltjes integral
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I redirected Stieltjes integral here, as it seems to mean the same as "Riemann-Stieltjes integral". Here is a copy of what was in the now-redirected article. Jon Olav Vik 12:10, 4 November 2005 (UTC)
The Stieltjes integral provides a direct way of (numerically) defining an integral of the type
without first having to convert it to
and then integrating this converted form by means of a pre-existing, non-Stieltjes integration method.
Stieltjes integration provides a means of extending any type of integration of the form
such as Riemann integration, Darboux integration, or Lebesgue integration.
Thus, the form
can be integrated by means of Riemann-Stieltjes integration, Darboux-Stieltjes integration, or Lebesgue-Stieltjes integration. Function f is called the integrand and function g is called the integrator.
[edit] See also
[edit] absolute continuity
A discussion of absolute continuity is needed on these pages. It addresses the question: when is a function the integral of its (a.e.) defined derivative?
