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

• Autorzy: Anders Nilsson , Peter Wingren
• Języki publikacji: EN

Abstrakty

EN

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, $2^{-n} ≤ H^{r}(K) ≤ 2n^{r/2}$.

Kategorie tematyczne

• 28A78: Hausdorff and packing measures
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 181
• Numer: 3
• Strony: 285-296

Daty

wydano

2007

Twórcy

autor

Anders Nilsson

• Department of Mathematics and Mathematical Statistics, Umeå University, 901 87 Umeå, Sweden

autor

Peter Wingren

• Department of Mathematics and Mathematical Statistics, Umeå University, 901 87 Umeå, Sweden

Identyfikatory

DOI

10.4064/sm181-3-5