2014
DOI: 10.1090/s0002-9939-2014-11962-9
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On packing measures and a theorem of Besicovitch

Abstract: Abstract. Let Hh be the h-dimensional Hausdorff measure on R d . Besicovitch showed that if a set E is null for H h , then it is null for H g , for some dimension g smaller than h. We prove that this is not true for packing measures. Moreover, we consider the corresponding questions for sets of non-σ-finite packing measure, and for pre-packing measure instead of packing measure.

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