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

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints