On dimensions of tangent cones in limit spaces with lower Ricci curvature bounds

We show that if X is a limit of n -dimensional Riemannian manifolds with Ricci curvature bounded below and gamma is a limit geodesic in X , then along the interior of gamma same scale measure metric tangent cones T gamma(t)X are Holder continuous with respect to measured Gromov-Hausdorff topology and have the same dimension in the sense of Colding-Naber.