info prev up next book cdrom email home

Lebesgue-Stieltjes Integral

Let $\alpha(x)$ be a monotone increasing function and define an Interval $I=(x_1, x_2)$. Then define the Nonnegative function


The Lebesgue Integral with respect to a Measure constructed using $U(I)$ is called the Lebesgue-Stieltjes integral, or sometimes the Lebesgue-Radon Integral.


Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 326, 1980.

© 1996-9 Eric W. Weisstein