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.