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arXiv · 1205.6224

On packing measures and a theorem of Besicovitch

Ignacio García·Pablo Shmerkin
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Abstract

Besicovitch showed that if a set is null for the Hausdorff measure associated to a given dimension function, then it is still null for the Hausdorff measure corresponding to a smaller dimension function. We prove that this is not true for packing measures. Moreover, we consider the corresponding questions for sets of non-$\sigma$-finite packing measure, and for pre-packing measure instead of packing measure.

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Ignacio García, Pablo Shmerkin. 2012-05-28. On packing measures and a theorem of Besicovitch. https://arxiv.org/abs/1205.6224

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