Topologies for the Space ofBV-Integrable Functions in RN

We introduce two topologies on the space ofBV-integrable functions in RN. Among the studied properties are barrelledness and integral representation of linear continuous functionals. In one case, we characterize the dual space. We show the relations with the study of multipliers. Finally, we also introduce and study a topology on the space of boundedBVfunctions in RN.