Expo. Math. 30, 412-418 (2012) [DOI: 10.1016/j.exmath.2012.09.002]

On the Substitution Rule for Lebesgue-Stieltjes Integrals

Neil Falkner and Gerald Teschl

We show how two change-of-variables formulæ for Lebesgue-Stieltjes integrals generalize when all continuity hypotheses on the integrators are dropped. We find that a sort of “mass splitting phenomenon” arises.

MSC2010: Primary 26A42, 26A48; Secondary 28A25, 28-01
Keywords: Lebesgue-Stieltjes integrals, substitution rule, generalized inverse

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