Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below

We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence. In particular, the limiting current is essentially unique, has multiplicity one, and mass equal to the Hausdorff measure. Moreover, the limit spaces satisfy a constancy theorem.