Homogeneity and non-coincidence of Hausdorff and box dimensions for subsets of ℝⁿ

Anders Nilsson, and Peter Wingren. "Homogeneity and non-coincidence of Hausdorff and box dimensions for subsets of ℝⁿ." Studia Mathematica 181.3 (2007): 285-296. <http://eudml.org/doc/284467>.

@article{AndersNilsson2007,
abstract = {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 $(dim_\{H\}(U), \underline\{dim\}_\{B\}(U), \overline\{dim\}_\{B\}(U)) = (r,s,t)$. Moreover, $2^\{-n\} ≤ H^\{r\}(K) ≤ 2n^\{r/2\}$.},
author = {Anders Nilsson, Peter Wingren},
journal = {Studia Mathematica},
keywords = {fractal; Cantor set construction; homogeneous; Hausdorff dimension; box dimension; packing dimension},
language = {eng},
number = {3},
pages = {285-296},
title = {Homogeneity and non-coincidence of Hausdorff and box dimensions for subsets of ℝⁿ},
url = {http://eudml.org/doc/284467},
volume = {181},
year = {2007},
}

TY - JOUR
AU - Anders Nilsson
AU - Peter Wingren
TI - Homogeneity and non-coincidence of Hausdorff and box dimensions for subsets of ℝⁿ
JO - Studia Mathematica
PY - 2007
VL - 181
IS - 3
SP - 285
EP - 296
AB - 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 $(dim_{H}(U), \underline{dim}_{B}(U), \overline{dim}_{B}(U)) = (r,s,t)$. Moreover, $2^{-n} ≤ H^{r}(K) ≤ 2n^{r/2}$.
LA - eng
KW - fractal; Cantor set construction; homogeneous; Hausdorff dimension; box dimension; packing dimension
UR - http://eudml.org/doc/284467
ER -