Packing Measure in General Metric Space

Abstract

Packing measures are counterparts to Hausdorff measures, used in measuring fractal dimension of sets. C. Tricot defined them for subsets of finite-dimensional Euclidean space. We consider here the proper way to phrase the definitions for use in general metric spaces, and for Hausdorff functions other than the simple powers, in particular non-blanketed Hausdorff functions. The question of the Vitali property arises in this context. An example of a metric space due to R. O. Davies illustrates the concepts.