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Dimension prints of fractal sets
Author(s) -
Reyes M.,
Rogers C. A.
Publication year - 1994
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007191
Subject(s) - mathematics , packing dimension , hausdorff dimension , minkowski–bouligand dimension , inductive dimension , cartesian product , effective dimension , dimension (graph theory) , dimension function , fractal dimension , lebesgue covering dimension , dimension theory (algebra) , lebesgue measure , fractal dimension on networks , lebesgue integration , correlation dimension , complex dimension , fractal , pure mathematics , discrete mathematics , mathematical analysis , fractal analysis
Dimension prints were developed in 1988 to distinguish between different fractal sets in Euclidean spaces having the same Hausdorff dimension but with very different geometric characteristics. In this paper we compute the dimension prints of some fractal sets, including generalized Cantor sets on the unit circle S 1 in ℝ 2 and the graphs of generalized Lebesgue functions, also in ℝ 2 . In this second case we show that the dimension print for the graphs of the Lebesgue functions can approach the maximal dimension print of a set of dimension 1. We study the dimension prints of Cartesian products of linear Borel sets and obtain the exact dimension print when each linear set has positive measure in its dimension and the dimension of the Cartesian product is the sum of the dimensions of the factors.