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Recouvrements, derivation des mesures et dimensions

2006
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Revista matemática iberoamericana
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Let X be a set with a symmetric kernel d (not necessarily a distance). The space (X, d) is said to have the weak (resp. strong) covering property of degree ≤ m [briefly prf (m) (resp. prF(m))], if, for each family B of closed balls of (X, d) with radii in a decreasing sequence (resp. with bounded radii), there is a subfamily, covering the center of each element of B , and of order ≤ m (resp. spliting into m disjoint families). Since Besicovitch, covering properties are known to be the main tool

doi:10.4171/rmi/478
fatcat:e362c3ynzfbfdd6p2relfqkrja