Integrating with respect to functions which are constant on intervals whose bounds are discontinuity

points (of those functions) is frequent in many branches of Mathematics, specially in stochastic

processes. For such functions and alike extension, a comparison between Riemann-Stieltjes and

Lebesgue-Stieltjes integration and the integrals formulas leads to interesting facts for students (as

complements of Measure Theory and Integrations) and for practitioners and and researchers. We

undergone conditions of existence the Riemann-Stieltjes integrals related to that type of function

and compare the results with what should be expected for Lebesgue-Stieltjes theory.

**Author (s) Details **

**Gane Samb Lo**

LERSTAD, Gaston Berger University, Saint-Louis, Senegal and LSTA, Pierre and Marie Curie University, Paris VI, France and AUST – African University of Science and Technology, Abuja, Nigeria.

**Aladji Babacar Niang**

LERSTAD, Gaston Berger University, Saint-Louis, Senegal.

**Cherif Mamadou Moctar Traore**

LERSTAD, Gaston Berger University, Saint-Louis, Senegal and LMA/USTTB – Univestide des Sciences, Techniques et Technologies de Bamako, Mali.

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