  In this paper we show existence of traces of functions of bounded variation
on the boundary of a certain class of domains in metric measure spaces equipped
with a doubling measure supporting a $1$-Poincar\'e inequality, and obtain
$L^1$ estimates of the trace functions. In contrast with the treatment of
traces given in other papers on this subject, the traces we consider do not
require knowledge of the function in the exterior of the domain. We also
establish a Maz'ya-type inequality for functions of bounded variation that
vanish on a set of positive capacity.
