caa a22 4500 445868791 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00605-010-0271-3 doi (NATIONALLICENCE)springer-10.1007/s00605-010-0271-3 Rajala Tapio Department of Mathematics and Statistics, 40014 University of Jyväskylä, P. O. Box 35 (MaD), Jyväskylä, Finland aut Comparing the Hausdorff and packing measures of sets of small dimension in metric spaces [Elektronische Daten] [Tapio Rajala] 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 $${E\subset X}$$ 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 $${\mathbb{R}^n}$$. Springer-Verlag, 2010 Hausdorff measure nationallicence Packing measure nationallicence Density nationallicence Metric space nationallicence Monatshefte für Mathematik Springer Vienna 164/3(2011-11-01), 313-323 0026-9255 164:3<313 2011 164 605 https://doi.org/10.1007/s00605-010-0271-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0271-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rajala Tapio Department of Mathematics and Statistics, 40014 University of Jyväskylä, P. O. Box 35 (MaD), Jyväskylä, Finland aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 164/3(2011-11-01), 313-323 0026-9255 164:3<313 2011 164 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer