The Hausdorff and packing measure of some digital expansions
Daniel Ingebretson
TL;DR
This paper calculates the precise Hausdorff and packing measures for certain real number sets characterized by digital expansions that omit digits beyond a specific threshold, providing exact measure values.
Contribution
It introduces exact measure computations for sets defined by digit restrictions in digital expansions, advancing understanding of their fractal properties.
Findings
Exact Hausdorff measure values derived for the sets.
Exact packing measure values derived for the sets.
Provides new insights into the fractal structure of digit-restricted sets.
Abstract
We compute the exact Hausdorff and packing measure of sets of real numbers whose digital expansions in a given base are missing the digits beyond a given threshold.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Digital Image Processing Techniques · Mathematical Dynamics and Fractals