Linear bounded functionals on the space of regular regulated functions. (English) Zbl 0920.46031
A real-valued function defined on a compact interval is called regulated, if it has left and right side limits in every point and it is called regular, if the value in any point is the arithmetical mean of these two limits. The aim of the paper is to derive a representation of the dual space to the space of all regular, regulated functions. The representation is given by means of the Perron-Stieltjes integral.
Reviewer: Beloslav Riečan (Bratislava)
MSC:
46E99 | Linear function spaces and their duals |
26A39 | Denjoy and Perron integrals, other special integrals |
26A45 | Functions of bounded variation, generalizations |