  Under the definition of Ricci curvature bounded below for Alexandrov spaces
introduced by Zhang-Zhu, we generalize a result by Colding that an n
dimentional manifold with Ricci curvature greater or equal to n minus 1 and
volume close to that of the unit n sphere is close (in the Gromov-Hausdorff
distance) to the sphere, from the case of Riemannian manifolds to the case of
Alexandrov spaces, with an additional assumption, roughly speaking, that the
rough volume of the set of short cut points is small, following the basic idea
in the Riemannian case with necessary modifications because of the only almost
everywhere second differentiability of distance functions.
