We call a Gromov–Hausdorff limit of complete Riemannian manifolds with a lower bound of Ricci curvature a Ricci limit space. Furthermore, we prove that any Ricci limit space has integral Hausdorff dimension, provided that its Hausdorff dimension is not greater than 2. We also classify -dimensional Ricci limit spaces.
"On low-dimensional Ricci limit spaces." Nagoya Math. J. 209 1 - 22, March 2013. https://doi.org/10.1215/00277630-1959442