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

\int_a^b f(x) \, d g(x)

without first having to convert it to

\int_a^b f(x) \, g'(x) \, dx

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

\int_a^b f(x) \, dx,

such as Riemann integration, Darboux integration, or Lebesgue integration.

Thus, the form

\int_a^b f(x) \, d g(x)

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

Category:Integral calculus

[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?

[edit] contributions?

Considering I just wrote a paper for my real analysis class that got a perfect score from my professor, should I do anything with it? I've only begun trying to contribute to Wikipedia so I'm trying to not make any blunders. Here's a link [1]. - Anastas5425 21:16, 23 April 2007 (UTC)