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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

\begin{displaymath}
U(I)=\alpha(x_2+0)-\alpha(x_1+0).
\end{displaymath}

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


References

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




© 1996-9 Eric W. Weisstein
1999-05-26