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• # Artykuł - szczegóły

## Studia Mathematica

2004 | 165 | 2 | 125-134

## Some properties of packing measure with doubling gauge

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.

125-134

wydano
2004

### Twórcy

autor
• Department of Mathematics, Hubei University, Hubei, 430062, P.R. China
autor
• Department of Mathematics, Tsinghua University, Beijing, 100084, P.R. China