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Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
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In this paper, we prove that on a compact, 
$n$-dimensional Alexandrov space with curvature at least −1, the Wasserstein barycenter of Borel probability measures 
${{\mu }_{1}},\ldots ,{{\mu }_{m}}$ is absolutely continuous with respect to the $n$-dimensional Hausdorff measure if one of them is.
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