Approximation Theory and Its Applications

, Volume 17, Issue 1, pp 70–75 | Cite as

The Integral Formula for Calculating the Hausdorff Measure of Some Fractal Sets

  • Lu Shipan
  • Su Weiyi


It is important to calculate the Hausdorff dimension and the Hausdorff mesure respect to this dimension for some fractal sets. By using the usual method of “Mass Distribution”, we can only calculate the Hausdorff dimension. In this paper, we will construct an integral formula by using lower inverse s-density and then use it to calculate the Hausdorff measures for some fractional dimensional sets.


Mass Distribution Integral Formula Hausdorff Dimension Usual Method Hausdorff Measure 
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    Falconer, K. J., The Geometry of Fractal Sets, Combridge Univ. Press, 1985.Google Scholar
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    Falconer, K. J., Fractal Geometry, John Wiley and Sons, 1990.Google Scholar
  3. [3]
    Baek, I. S., Dimensions of the Perturbed Cantor Set, Real Analysis Exchange, 19:1(1993–1994).Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Lu Shipan
    • 1
  • Su Weiyi
    • 2
  1. 1.Department of Mathematics Teacher's CollegeJimei UniversityXiamenChina
  2. 2.Department of MathematicsNanjing UniversityNanjingChina

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