MATHEMATICA BOHEMICA, Vol. 131, No. 1, pp. 1-9 (2006)

The dual of the space of functions
of bounded variation

Khaing Khaing Aye, Peng Yee Lee

Khaing Khaing Aye, (1) Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1, Nanyang Walk, Singapore 637616, (2) Department of Engineering Mathematics, Yangon Technological University, Yangon, Myanmar, e-mail: wk.ygn@mptmail.net.mm; Peng Yee Lee, Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1, Nanyang Walk, Singapore 637616, e-mail: pylee@nie.edu.sg

Abstract: In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.

Keywords: bounded variation, two-norm space, dual space, linear functional, Henstock integral, Stieltjes integral, regulated function

Classification (MSC2000): 26A39, 26A42, 26A45, 46B26, 46E99

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