The dual of the space of regulated functions in several variables

Yunyun Yang, Ricardo Estrada
2013 Sarajevo Journal of Mathematics  
We consider a class of regulated functions of several variables, namely, the class of functions φ defined in an open set U ⊂ R n such that at each x0 ∈ U the "thick" limit exists uniformly on w ∈ S, the unit sphere of R n , and such that φx 0 is a continuous function of w at each x0 ∈ 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
more » ... ons concentrated at a countable set. 2010 Mathematics Subject Classification. 28C05, 26B05, 26B35.
doi:10.5644/sjm.09.2.05 fatcat:6va2sroxvfhcddvnbxttmtofui