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• W2033339336 abstract "We give a new estimate for the ratio of s-dimensional Hausdorff measure ({mathcal{H}^s}) and (radius-based) packing measure ({mathcal{P}^s}) of a set in any metric space. This estimate is$$ inf_{E}frac{mathcal{P}^s(E)}{mathcal{H}^s(E)}ge 1+left(2-frac{3}{2^{1/s}}right)^s, $$where 0 < s < 1/2 and the infimum is taken over all metric spaces X and sets ({Esubset X}) with ({0 < mathcal{H}^s(E) < infty}). As an immediate consequence we improve the upper bound for the lower s-density of such sets in ({mathbb{R}^n})." @default.
• W2033339336 created "2016-06-24" @default.
• W2033339336 creator A5041041984 @default.
• W2033339336 date "2010-12-10" @default.
• W2033339336 modified "2023-10-17" @default.
• W2033339336 title "Comparing the Hausdorff and packing measures of sets of small dimension in metric spaces" @default.
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• W2033339336 doi "https://doi.org/10.1007/s00605-010-0271-3" @default.
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