ON CANTOR SETS AND PACKING MEASURES

WEI, CHUN; WEN, SHENG-YOU

doi:10.4134/BKMS.2015.52.5.1737

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ON CANTOR SETS AND PACKING MEASURES

Journal title : Bulletin of the Korean Mathematical Society
Volume 52, Issue 5, 2015, pp.1737-1751
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2015.52.5.1737

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 ${$H^g$}$ -measure, ${$P^g$}$ -measure, and ${$P^g_0$}$ -premeasure. Also, we show that every compact metric space of infinite ${$P^g_0$}$ -premeasure has a compact countable subset of infinite ${$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

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