Inserted: 4 jul 2019
Last Updated: 4 jul 2019
Following a Maz'ya-type approach, we re-adapt the theory of rough traces of functions of bounded variation ($BV$) in the context of doubling metric measure spaces supporting a Poincaré inequality. This eventually allows for an integration by parts formula involving the rough trace of such a function. We then compare our analysis with the discussion done in a recent work by P. Lahti and N. Shanmugalingam, where traces of $BV$ functions are studied by means of the more classical Lebesgue-point characterization, and we determine the conditions under which the two notions coincide.