【摘 要】
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In this paper we discuss the relations among the doubling condition, equivalence of the Hausdorff measures and equivalence of metrics. We will show that H ρ,g1
【机 构】
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Nonlinear Scientific Center,Department of Mathematics
论文部分内容阅读
In this paper we discuss the relations among the doubling condition, equivalence of the Hausdorff measures and equivalence of metrics. We will show that H ρ,g1 and H ρ,g2 are equivalent for any compact metric space (X,ρ) if and only if g1 and g2 are equivalent gauge functions. Then, we prove that for given c∈(0,∞)\{1}, H ρ,g and H cρ,g are equivalent for any compact metric space (X,ρ) if and only if the gauge function g satisfies the doubling condition, where H ρ,g is the Hausdorff measure with respect to the metric ρ and gauge function g.
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