Let $(M^{n}_{j},d_{j},p_{j})\stackrel{{\scriptstyle d_{GH}}}{{\longrightarrow}}(X,d,p)$ be a Gromov-Hausdorff limit of manifolds with $|{\rm Ric}_{M^{n}_{j}}|\leq n-1$ and ${\rm Vol}(B_{1}(p_{j}))>{\rm v}>0$. Then the singular set $\mathcal{S}$ satisfies

$\displaystyle\dim\mathcal{S}\leq n-4.$

(1.4)

The dimension can be taken to be the Hausdorff or Minkowski dimension.