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Conditions for equality of Hausdorff and packing measures on ℝ
, 1996 This note answers the question, for which Hausdorff functions \(h\) may the \(h\)-Hausdorff and \(h\)-packing measures agree on some subset \(A\) of \(\mathbb{R}^n\), and be positive and finite. We show that these conditions imply that \(h\) is a regular density function, in the sense of Preiss, and that for each such function there is a subset of ...
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Self-similar sets of Hausdorff measure zero and positive packing measure
, 2013 A contractive similarity is a function which preserves the geometry of a object but shrinks it down by some factor. If we have a finite collection of similarities, then there exists a unique compact set K which is the same set as the union of the the images of K under each similarity. This kind of K is called a self-similar set, which is a certain type
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, 2002 秦野, 薫
core
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