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.