Geodesic
The Hausdorff and Packing Dimensions of Some Sets Related to Sierpiński Carpets
Canadian journal of mathematics, Tome 51 (1999) no. 5, pp. 1073-1088

Voir la notice de l'article provenant de la source Cambridge University Press

The Sierpiński carpets first considered by C.McMullen and later studied by Y. Peres are modified by insisting that the allowed digits in the expansions occur with prescribed frequencies. This paper (i) calculates the Hausdorff, box (or Minkowski), and packing dimensions of the modified Sierpiński carpets and (ii) shows that for these sets the Hausdorff and packing measures in their dimension are never zero and gives necessary and sufficient conditions for these measures to be infinite.
DOI : 10.4153/CJM-1999-047-4
Mots-clés : 28A78, 28A80 
Nielsen, Ole A. The Hausdorff and Packing Dimensions of Some Sets Related to Sierpiński Carpets. Canadian journal of mathematics, Tome 51 (1999) no. 5, pp. 1073-1088. doi: 10.4153/CJM-1999-047-4
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