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New Inequalities on Fractal Analysis and Their Applications

Abstract

Two new fractal measures and are constructed from Minkowski contents and. The properties of these two new measures are studied. We show that the fractal dimensions Dim and can be derived from and, respectively. Moreover, some inequalities about the dimension of product sets and product measures are obtained.

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Correspondence to Der-Chen Chang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Chang, DC., Xu, Y. New Inequalities on Fractal Analysis and Their Applications. J Inequal Appl 2007, 026249 (2007). https://doi.org/10.1155/2007/26249

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Keywords

  • Fractal Dimension
  • Fractal Analysis
  • Product Measure
  • Fractal Measure
  • Minkowski Content
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