The dual of the space of regulated functions in several variables

Abstract

We consider a class of regulated functions of several vari- ables, namely, the class of functions dened in an open set U R n such that at each x02 U the \thick limit x0 (w) = lim !0+ (x 0 +w) ; exists uniformly on w2 S; the unit sphere of R n ; and such that x0 is a continuous function of w at each x02 U: We identify the elements of the dual spaces of several Banach space of such regulated functions in several variables as signed measures with absolutely convergent sums of \thick delta functions concentrated at a countable set.