Khaing Aye Khaing, Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1, Nanyang Walk, Singapore 637616; Department of Engineering Mathematics, Yangon Technological University, Yangon, Myanmar, e-mail: khaing@ixna.com; Lee Peng Yee, Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1, Nanyang Walk, Singapore 637616, e-mail: pylee@nie.edu.sg
Abstract: In this paper we give a representation theorem for the orthogonally additive functionals on the space $BV$ in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.
Keywords: functional, orthogonally additive functional, two-norm space, function of bounded variation, Henstock integral, Stieltjes integral
Classification (MSC2000): 46A70, 26A45, 26A39, 26A42
Full text of the article: