RELATIONS BETWEEN PACKING PREMEASURE AND MEASURE ON METRIC SPACE |
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| Authors: | Wen Shengyou Wu Min |
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| Institution: | aDepartment of Mathematics, Hubei University, Wuhan 430062, China;bDepartment of Mathematics, South China University of Technology, Guangzhou 510640, China |
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| Abstract: | Let X be a metric space and μ a finite Borel measure on X. Let and be the packing premeasure and the packing measure on X, respectively, defined by the gauge | , where q,t  R. For any compact set E of finite packing premeasure the authors prove: (1) if q ≤ 0 then if q > 0 and μ is doubling on E then and are both zero or neither.
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| Keywords: | Doubling condition packing premeasure packing measure |
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