Étant donné une mesure de probabilité sur un espace d’Alexandrov avec courbure minorée, nous prouvons que le support de la mesure poussée de sur le cône tangent à son barycentre (exponentiel) est un sous-ensemble d’un espace de Hilbert, sans condition de séparabilité du cône tangent.
Given a probability measure on an Alexandrov space with curvature bounded below, we prove that the support of the pushforward of on the tangent cone at its (exponential) barycenter is a subset of a Hilbert space, without separability of the tangent cone.
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Thibaut Le Gouic 1
@article{CRMATH_2020__358_4_489_0, author = {Thibaut Le Gouic}, title = {A note on flatness of non separable tangent cone at a barycenter}, journal = {Comptes Rendus. Math\'ematique}, pages = {489--495}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {4}, year = {2020}, doi = {10.5802/crmath.66}, language = {en}, }
Thibaut Le Gouic. A note on flatness of non separable tangent cone at a barycenter. Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 489-495. doi : 10.5802/crmath.66. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.66/
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