Let 
be a monotone increasing function and define an interval 
.
Then define the nonnegative function
The Lebesgue integral with respect to a measure constructed using 
is called the Lebesgue-Stieltjes integral, or sometimes
the Lebesgue-Radon integral.
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References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 354, 1980.Referenced
on Wolfram|Alpha
Lebesgue-Stieltjes Integral
Cite this as:
Weisstein, Eric W. "Lebesgue-Stieltjes Integral."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Lebesgue-StieltjesIntegral.html
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