Rough traces of BV functions in metric measure spaces

Following a Maz’ya-type approach, we adapt the theory of rough traces of functionsof bounded variation (BV) to the context of doubling metric measure spaces supporting a Poincaréinequality. This eventually allows for an integration by parts formula involving the rough traceof such functions. We then compare our analysis with the study done in a recent work by Lahtiand Shanmugalingam, where traces ofBVfunctions are studied by means of the more classicalLebesgue-point characterization, and we determine the conditions under which the two notionscoincide.