  We consider non-linear elliptic equations having a measure in the right hand
side, of the type $ \divo a(x,Du)=\mu, $ and prove differentiability and
integrability results for solutions. New estimates in Marcinkiewicz spaces are
also given, and the impact of the measure datum density properties on the
regularity of solutions is analyzed in order to build a suitable
Calder\'on-Zygmund theory for the problem. All the regularity results presented
in this paper are provided together with explicit local a priori estimates.
