Stieltjes integral

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Stieltjes integral [′stēlt·yəs ‚int·ə·grəl]

(mathematics)

The Stieltjes integral of a real function ƒ(x) relative to a real functiong(x) of bounded variation on an interval [a,b] is defined, analogously to the Riemann integral, as a limit of a sum of terms ƒ(a_i) [g(x_i) - g(x_i-1)] taken as partitions of the interval shrink. DenotedAlso known as Riemann-Stieltjes integral.

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Lebesgue-Stieltjes integral

Riemann-Stieltjes integral

Stieltjes transform

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