# Looking for a proof of a dominated convergence theorem for Lebesgue-Stieltjes integrals

From what I've read there exists a similar theorem to the dominated convergence theorem for Lebesgue integrals, which is applicable to Lebesgue-Stieltjes integrals.

Does someone have a statement of this theorem and if possible a proof for me? I haven't been able to find anything so far.

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Aren't Lebesgue-Stieltjes integrals Lebesgue integrals by definition? –  Antonio Vargas Feb 17 '13 at 20:28
I thought that was only for continuous functions. –  BallzofFury Feb 17 '13 at 20:46
The wiki page defines Lebesgue-Stieltjes integrals of bounded, Borel-measurable functions as a finite sum of Lebesgue integrals. –  Antonio Vargas Feb 17 '13 at 20:51