Some properties of packing measure with doubling gauge

Sheng-You Wen; Zhi-Ying Wen

Studia Mathematica, Tome 162 (2004), p. 125-134 / Harvested from The Polish Digital Mathematics Library

Résumé

Let g be a doubling gauge. We consider the packing measure $^{g}$ and the packing premeasure $₀^{g}$ in a metric space X. We first show that if $₀^{g} (X)$ is finite, then as a function of X, $₀^{g}$ has a kind of “outer regularity”. Then we prove that if X is complete separable, then $λ s u p ₀^{g} (F) \leq^{g} (B) \leq s u p ₀^{g} (F)$ for every Borel subset B of X, where the supremum is taken over all compact subsets of B having finite $₀^{g}$ -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.

Publié le : 2004-01-01

Zbl 1055.28004

EUDML-ID : urn:eudml:doc:284678

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Sheng-You Wen; Zhi-Ying Wen. Some properties of packing measure with doubling gauge. Studia Mathematica, Tome 162 (2004) pp. 125-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-2-3/