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 -measure, -measure, and -premeasure. Also, we show that every compact metric space of infinite -premeasure has a compact countable subset of infinite -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 , and a doubling gauge g such that has different positive finite -measure and -premeasure.
Keywords
Cantor set;packing measure;premeasure;gauge function;doubling condition;
Language
English
Cited by
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