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  • Research Article
  • Open Access

New Inequalities on Fractal Analysis and Their Applications

Journal of Inequalities and Applications20072007:026249

  • Received: 26 September 2006
  • Accepted: 23 November 2006
  • Published:


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.


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


Authors’ Affiliations

Department of Mathematics, Georgetown University, Washington, DC 20057, USA
School of Computer science and Engineering, South China University of Technology, Guangzhou, 510640, China


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© D.-C. Chang and Y. Xu 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.