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A topological splitting theorem for weighted Alexandrov spaces
Under an infinitesimal version of the Bishop-Gromov relative volume
comparison condition for a measure on an Alexandrov space, we prove a
topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove
an isometric splitting theorem for Riemannian manifolds with singularities of
nonnegative (Bakry-Emery) Ricci curvature.Comment: 20 pages to appear in Tohoku Mathematical Journa
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