ON CANTOR SETS AND PACKING MEASURES

For every doubling gauge g, we prove that there is a Cantor set of positive finite Hg-measure, Pg-measure, and Pg 0 -premeasure. Also, we show that every compact metric space of infinite Pg 0 -premeasure has a compact countable subset of infinite Pg 0 -premeasure. In addition, we obtain a class of u...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2015, 52(5), , pp.1737-1751
Main Authors: WEI, CHUN, WEN, SHENG-YOU
Format: Article
Language:English
Subjects:
수학
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Summary:For every doubling gauge g, we prove that there is a Cantor set of positive finite Hg-measure, Pg-measure, and Pg 0 -premeasure. Also, we show that every compact metric space of infinite Pg 0 -premeasure has a compact countable subset of infinite Pg 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 F = E∪F, and a doubling gauge g such that E ∪ F has different positive finite Pg-measure and Pg 0 -premeasure. KCI Citation Count: 0
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.2015.52.5.1737