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G. A. Edgar
Centered densities and fractal measures
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Published: |
March 14, 2007 |
Keywords: |
Fractal, density, variation, Hausdorff function |
Subject: |
Primary 28A; Secondary 03E, 11K, 12D |
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Abstract
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. |
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Author information
Department of Mathematics, The Ohio State University, 231 West Eighteenth Avenue, Columbus, Ohio 43210
edgar@math.ohio-state.edu
http://www.math.ohio-state.edu/~edgar/ |
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