Lebesgue-Stieltjes integral

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Lebesgue-Stieltjes integral

[lə′beg ′stēlt·yəs ‚int·ə·grəl]
(mathematics)
A Lebesgue integral of the form where φ is of bounded variation; if φ(x) = x, it reduces to the Lebesgue integral of ƒ(x); if φ(x) is differentiable, it reduces to the Lebesgue integral of ƒ(x)φ′(x).