  We establish the rectifiability of measures satisfying a linear PDE
constraint. The obtained rectifiability dimensions are optimal for many usual
PDE operators, including all first-order systems and all second-order scalar
operators. In particular, our general theorem provides a new proof of the
rectifiability results for functions of bounded variations (BV) and functions
of bounded deformation (BD). For divergence-free tensors we obtain refinements
and new proofs of several known results on the rectifiability of varifolds and
defect measures.
