ON CANTOR SETS AND PACKING MEASURES

Title & Authors
ON CANTOR SETS AND PACKING MEASURES
WEI, CHUN; WEN, SHENG-YOU;

Abstract
For every doubling gauge g, we prove that there is a Cantor set of positive finite $\small{H^g}$-measure, $\small{P^g}$-measure, and $\small{P^g_0}$-premeasure. Also, we show that every compact metric space of infinite $\small{P^g_0}$-premeasure has a compact countable subset of infinite $\small{P^g_0}$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F} Keywords Cantor set;packing measure;premeasure;gauge function;doubling condition; Language English Cited by References 1. M. Csornyei, An example illustrating$P^g$(K)$\neqP^g_0\$ (K) for sets of finite pre-measure, Real Anal. Exchange 27 (2001/02), no. 1, 65-70.

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