On SBV dual, Indiana Univ. Math. J., 47(1), 1998. 99-121.
This paper addresses the question of describing the dual of the space of functions having bounded variation in Rn. In particular we are interested in how a linear continuous functional acts on the jump part of the distributional derivative of a BV function. It is shown that representing this action as the flux of an Hn-1 measurable vectorfield through the jump set is independent of ZFC. Analogous undecidable results about various spaces of 1 dimensional currents are stated. Finally we apply our results to obtain an improvement of Whitney's integral representation of flat cochains.