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

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Nilsson A., Wingren P.

Studia Mathematica

2007

tom 181

nr 3

285-296

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, $2^{-n} ≤ H^{r}(K) ≤ 2n^{r/2}$.

Ograniczanie wyników

1 Studia Mathematica

1 Nilsson A.

1 Wingren P.

1 2007

Wyniki wyszukiwania

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