New York Journal of Mathematics
Volume 13 (2007) 97-106


G. A. Edgar

Centered densities and fractal measures

Published: March 14, 2007
Keywords: Fractal, density, variation, Hausdorff function
Subject: Primary 28A; Secondary 03E, 11K, 12D

We have collected definitions and basic results for the (centered ball) density in metric space with respect to an arbitrary Hausdorff function. We have kept the definitions general: we do not assume the Hausdorff functions are continuous or blanketed, and we do not assume the metric space is a subset of Euclidean space. We discuss the covering measure (= centered Hausdorff measure) and packing measure defined from these densities.

Author information

Department of Mathematics, The Ohio State University, 231 West Eighteenth Avenue, Columbus, Ohio 43210