  For collapsing sequences of Riemannian manifolds which satisfy a uniform
lower Ricci curvature bound it is shown that there is a sequence of scales such
that for a set of good base points of large measure the pointed rescaled
manifolds subconverge to a product of a Euclidean and a compact space. All
Euclidean factors have the same dimension, all possible compact factors satisfy
the same diameter bounds and their dimension does not depend on the choice of
the base point (along a fixed subsequence).
