Some properties of packing measure with doubling gauge

被引:9
|
作者
Wen, SY [1 ]
Wen, ZY
机构
[1] Hubei Univ, Dept Math, Hubei 430062, Peoples R China
[2] Tsing Hua Univ, Dept Math, Beijing 100084, Peoples R China
关键词
packing measure; premeasure; gauge function; doubling condition;
D O I
10.4064/sm165-2-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let g be a doubling gauge. We consider the packing measure P-g and the packing premeasure P-0(g) in a metric space X. We first show that if P-0(g)(X) is finite, then as a function of X, P-0(g) has a kind of "outer regularity". Then we prove that if X is complete separable, then lambda sup P-0(g) (F) less than or equal to P-g (B) less than or equal to sup P-0(g) (F) for every Borel subset B of X, where the supremum is taken over all compact subsets of B having finite P-0(g)-premeasure, and lambda is a positive number depending only on the doubling gauge g. As an application, we show that for every doubling gauge function, there is a compact metric space of finite positive packing measure.
引用
收藏
页码:125 / 134
页数:10
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