In Alexandrov spaces with curvature bounded below, the pushforward of a probability measure to the tangent cone at its barycenter has support contained in a Hilbert space without requiring separability of the cone.
On tangent cones of Alexandrov space s with curvature bounded below
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A note on flatness of non separable tangent cone
In Alexandrov spaces with curvature bounded below, the pushforward of a probability measure to the tangent cone at its barycenter has support contained in a Hilbert space without requiring separability of the cone.