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Mass localization

Le : 10/02/2014 11h00
Par : Thibaut Le Gouic (Ecole centrale de Marseille)
Lieu : I 103
Lien web :
Résumé : For a given class F of closed sets of a measured metric space (E, d, μ), we want to find the smallest element B of the class F such that μ(B) ≥ 1 − α, for a given 0 < α < 1. This set B localizes the mass of μ. Replacing the measure μ by the empirical measure μn gives an empirical smallest set Bn . This talk introduces a formal definition of small sets (and their size) and study convergence of the set Bn to B in Hausdorff metric and their size.