eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2020-07-13 8 2 34 38 10.12691/tjant-8-2-3 TJANT2020823 article Nassar H. S. Haidar nhaidar@suffolk.edu 1 CRAMS: Center for Research in Applied Mathematics & Statistics, AUL, Beirut, Lebanon A conditioned equivalence is proved for a certain weighted Sobolev space to the space of Riemann integrable functions. An equivalence representing a new result that not only asserts the sufficiency (but non-necessity) nature of bounded variation of functions for their Riemann integrability, but also reveals a potential for some novel computational findings. http://pubs.sciepub.com/tjant/8/2/3/tjant-8-2-3.pdf bounded variation Sobolev space Stieltjes integrals continuity of functions Riemann integrability