The dual of the space of functions of bounded variation. (English) Zbl 1112.26008

Aye, Khaing Khaing; Lee, Peng Yee

Math. Bohem. 131, No. 1, 1-9 (2006).

Summary: 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.

MSC:

26A39	Denjoy and Perron integrals, other special integrals
26A42	Integrals of Riemann, Stieltjes and Lebesgue type
26A45	Functions of bounded variation, generalizations
46B26	Nonseparable Banach spaces
46E99	Linear function spaces and their duals

Keywords:

two-norm space; dual space; linear functional; Henstock integral; Stieltjes integral; regulated function