  A result of Larsen concerning the structure of the approximate gradient of
certain sequences of functions with Bounded Variation is used to present a
short proof of Ambrosio's lower semicontinuity theorem for quasiconvex bulk
energies in $SBV$. It enables to generalize to the $SBV$ setting the
decomposition lemma for scaled gradients in dimension reduction and also to
show that, from the point of view of bulk energies, $SBV$ dimensional reduction
problems can be reduced to analogue ones in the Sobolev spaces framework.
