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About: Exterior dimension     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatFractals, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: yago:Abstraction100002137yago:Cognition100023271yago:Form105930736yago:Fractal105931152yago:PsychologicalFeature100023100yago:Structure105726345yago:WikicatFractals New Facet based on Instances of this Class

In geometry, exterior dimension is a type of dimension that can be used to characterize the scaling behavior of "fat fractals".A fat fractal is defined to be a subset of Euclidean space such that, for every point of the set and every sufficiently small number ,the ball of radius centered at contains both a nonzero Lebesgue measure of points belonging to the fractal, and a nonzero Lebesgue measure of points that do not belong to the fractal. For such a set, the Hausdorff dimension is the same as that of the ambient space.