The Riemannian structure of Alexandrov spaces

@article{Otsu1994TheRS,
  title={The Riemannian structure of Alexandrov spaces},
  author={Yukio Otsu and Takashi Shioya},
  journal={Journal of Differential Geometry},
  year={1994},
  volume={39},
  pages={629-658}
}
Let X be an n -dimensional Alexandrov space of curvature bounded from below. We define the notion of singular point in X , and prove that the set S χ of singular points in X is of Hausdorff dimension < n - 1 and that X - S x has a natural C°-Riemannian structure. 
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