Characterization of local dimension functions of subsets of $ℝ^{d}$

• Autorzy: L. Olsen
• Języki publikacji: EN

Abstrakty

EN

For a subset $E ⊆ ℝ^{d}$ and $x ∈ ℝ^{d}$, the local Hausdorff dimension function of E at x is defined by
$dim_{H,loc}(x,E) = lim_{r↘ 0} dim_{H}(E ∩ B(x,r))$
where $dim_{H}$ denotes the Hausdorff dimension. We give a complete characterization of the set of functions that are local Hausdorff dimension functions. In fact, we prove a significantly more general result, namely, we give a complete characterization of those functions that are local dimension functions of an arbitrary regular dimension index.

Kategorie tematyczne

• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 103
• Numer: 2
• Strony: 231-239

Daty

wydano

2005

Twórcy

autor

L. Olsen

• Department of Mathematics, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland

Identyfikatory

DOI

10.4064/cm103-2-8