Acta mathematica scientia,Series B
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Wen Shengyou; Wu Min
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Abstract:
Let X be a metric space and [[mu]] a finite Borel measure on X. Let $\bar{\mathcal{P}}_{\mu}^{q,t}$ and ${\mathcal{P}}_{\mu}^{q,t}$ be the packing premeasure and the packing measure on $X$, respectively, defined by the gauge $(\mu B(x,r))^q(2r)^t$, where $q,t\in\mathbb{R}$. For any compact set $E$ of finite packing premeasure the authors prove: (1) if $q\leq 0$ then $\bar{\mathcal{P}}_\mu^{q,t}(E)={\mathcal{P}}_\mu^{q,t}(E)$; (2) if $q>0$ and $\mu$ is doubling on $E$ then $\bar{\mathcal{P}}_\mu^{q,t}(E)$ and ${\mathcal{P}}_\mu^{q,t}(E)$ are both zero or neither.
Key words: Doubling condition, packing premeasure, packing measure
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Wen Shengyou; Wu Min. RELATIONS BETWEEN PACKING PREMEASURE AND MEASURE ON METRIC SPACE[J].Acta mathematica scientia,Series B, 2007, 27(1): 137-144.
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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(07)60012-5
http://121.43.60.238/sxwlxbB/EN/Y2007/V27/I1/137
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