Lebesgue-Stieltjes integral

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).