On the substitution rule for Lebesgue-Stieltjes integrals
Neil Falkner, Gerald Teschl
TL;DR
This paper explores generalized change-of-variables formulas for Lebesgue-Stieltjes integrals without continuity assumptions, revealing a mass splitting phenomenon that affects the integral's behavior.
Contribution
It extends existing formulas for Lebesgue-Stieltjes integrals to cases with discontinuous integrators, uncovering a new mass splitting phenomenon.
Findings
Generalized change-of-variables formulas without continuity assumptions
Identification of a mass splitting phenomenon in Lebesgue-Stieltjes integrals
Implications for the analysis of discontinuous integrators
Abstract
We show how two change-of-variables formulae for Lebesgue-Stieltjes integrals generalize when all continuity hypotheses on the integrators are dropped. We find that a sort of "mass splitting phenomenon" arises.
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