[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2015.52.5.1737

ON CANTOR SETS AND PACKING MEASURES

WEI, CHUN (DEPARTMENT OF MATHEMATICS SOUTH CHINA UNIVERSITY OF TECHNOLOGY)
WEN, SHENG-YOU (DEPARTMENT OF MATHEMATICS HUBEI UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.52, no.5, 2015 , pp. 1737-1751 More about this Journal

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 $\bar{F}=E{\cup}F$ , and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$ -measure and $P^g_0$ -premeasure.

Keywords

Cantor set; packing measure; premeasure; gauge function; doubling condition;

Citations & Related Records

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