Homogeneity and non-coincidence of Hausdorff and box dimensions for subsets of ℝⁿ
Anders Nilsson ; Peter Wingren
Studia Mathematica, Tome 178 (2007), p. 285-296 / Harvested from The Polish Digital Mathematics Library
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A class of subsets of ℝⁿ is constructed that have certain homogeneity and non-coincidence properties with respect to Hausdorff and box dimensions. For each triple (r,s,t) of numbers in the interval (0,n] with r < s < t, a compact set K is constructed so that for any non-empty subset U relatively open in K, we have (dimH(U),dim̲B(U),dim¯B(U))=(r,s,t). Moreover, 2-n≤Hr(K)≤2nr/2.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:284467 
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Anders Nilsson; Peter Wingren. Homogeneity and non-coincidence of Hausdorff and box dimensions for subsets of ℝⁿ. Studia Mathematica, Tome 178 (2007) pp. 285-296. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-3-5/