B P International

A Comparative study between Riemann-Stieltjes and Lebesgue-Stieltjes Integration using Discrete Distribution Functions

Gane Samb Lo1,2,3*, Aladji Babacar Niang1 and Cherif Mamadou Moctar Traore1,4

1LERSTAD, Gaston Berger University, Saint-Louis, Senegal.
2LSTA, Pierre and Marie Curie University, Paris VI, France.
3AUST – African University of Science and Technology, Abuja, Nigeria.
4LMA/USTTB – Univestide des Sciences, Techniques et Technologies de Bamako, Mali.

Abstract

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.

Keywords: Riemann-Stieltjes integral; Lebesgue-Stieltjes integral; jump points and functions; integrability; integral formulas.

ISBN: 978-93-90149-72-8 (Print) | 978-93-90149-22-3 (eBook)

Chapter DOI: https://doi.org/10.9734/bpi/tpmcs/v1/5055D

Volume DOI: https://doi.org/10.9734/bpi/tpmcs/v1

Published: August 17, 2020

Complete book available here: http://bp.bookpi.org/index.php/bpi/catalog/book/237