  In a series of papers, including the present one, we give a new, shorter
proof of Almgren's partial regularity theorem for area minimizing currents in a
Riemannian manifold, with a slight improvement on the regularity assumption for
the latter. This note establishes a new a priori estimate on the excess measure
of an area minimizing current, together with several statements concerning
approximations with Lipschitz multiple valued graphs. Our new a priori estimate
is an higher integrability type result, which has a counterpart in the theory
of Dir-minimizing multiple valued functions and plays a key role in estimating
the accuracy of the Lipschitz approximations.
