Some properties of packing measure with doubling gauge

• Autorzy: Sheng-You Wen , Zhi-Ying Wen
• Języki publikacji: EN

Abstrakty

EN

Let g be a doubling gauge. We consider the packing measure $𝓟^{g}$ and the packing premeasure $𝓟₀^{g}$ in a metric space X. We first show that if $𝓟₀^{g}(X)$ is finite, then as a function of X, $𝓟₀^{g}$ has a kind of "outer regularity". Then we prove that if X is complete separable, then $λsup𝓟₀^{g}(F) ≤ 𝓟^{g}(B) ≤ sup𝓟₀^{g}(F)$ for every Borel subset B of X, where the supremum is taken over all compact subsets of B having finite $𝓟₀^{g}$-premeasure, and λ is a positive number depending only on the doubling gauge g. As an application, we show that for every doubling gauge function, there is a compact metric space of finite positive packing measure.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 165
• Numer: 2
• Strony: 125-134

Daty

wydano

2004

Twórcy

autor

Sheng-You Wen

• Department of Mathematics, Hubei University, Hubei, 430062, P.R. China

autor

Zhi-Ying Wen

• Department of Mathematics, Tsinghua University, Beijing, 100084, P.R. China

Identyfikatory

DOI

10.4064/sm165-2-3