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, where q,t set membership, variant R. For any compact set E of finite packing premeasure the authors prove: (1) if q ≤ 0 then
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if q > 0 and μ is doubling on E then
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and
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are both zero or neither.
RELATIONS BETWEEN PACKING PREMEASURE AND MEASURE ON METRIC SPACE
作者姓名:文胜友  吴敏
作者单位:Department of Mathematics Hubei University,Department of Mathematics South China University of Technology Wuhan 430062,China,Guangzhou 510640,China
基金项目:Supported by Natural Science Foundation of China (10571063)
摘    要:Let X be a metric space andμa finite Borel measure on X. Let pμq,t and pμq,t be the packing premeasure and the packing measure on X, respectively, defined by the gauge (μB(x,r))q(2r)t, where q, t∈R. For any compact set E of finite packing premeasure the authors prove: (1) if q≤0 then pμq,t(E)=pμq,t(E);(2)if q>0 andμis doubling on E then pμq,t(E) and pμq,t(E) are both zero or neither.

关 键 词:度量空间  填充准测度  填充测度  相关性
收稿时间:2004-12-22

RELATIONS BETWEEN PACKING PREMEASURE AND MEASURE ON METRIC SPACE
Wen Shengyou,Wu Min.RELATIONS BETWEEN PACKING PREMEASURE AND MEASURE ON METRIC SPACE[J].Acta Mathematica Scientia,2007,27(1):137-144.
Authors:Wen Shengyou  Wu Min
Institution:aDepartment of Mathematics, Hubei University, Wuhan 430062, China;bDepartment of Mathematics, South China University of Technology, Guangzhou 510640, China
Abstract:Let X be a metric space and μ a finite Borel measure on X. Let
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and
View the MathML source
be the packing premeasure and the packing measure on X, respectively, defined by the gauge
(μB(x,r))q(2r)t
Keywords:Doubling condition  packing premeasure  packing measure
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