MATHEMATICA BOHEMICA, Vol. 129, No. 4, pp. 411-419 (2004)

Orthogonally additive functionals on $BV$

Khaing Aye Khaing, Peng Yee Lee

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

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