We introduce two topologies on the space of BV-integrable functions in R(N). Among the studied properties are barrelledness and integral representation of linear continuous Functionals. In one case, we charctcterize the dual space. We show the relations with the study of multipliers. Finally, we also introduce and study a topology on the space of bounded BV functions in R(N). (C) 1997 Academic Press. [References: 15]
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