Hausdorff dimension of the cantor set

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    Cantor Dimension Set
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SUMMARY

The Hausdorff dimension of the Cantor set, denoted as Hd(C), is definitively greater than 0, specifically calculated as d = log(2)/log(3). This conclusion is supported by the definition of Hausdorff measure, which provides the necessary framework for understanding the dimensional properties of fractals. The Cantor set serves as a classic example in fractal geometry, illustrating the concept of dimension beyond traditional Euclidean measures.

PREREQUISITES
  • Understanding of Hausdorff measure
  • Familiarity with fractal geometry concepts
  • Knowledge of logarithmic functions
  • Basic principles of measure theory
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  • Investigate the Cantor set's construction and its significance in topology
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Mathematicians, students of advanced geometry, and researchers interested in fractal analysis and measure theory will benefit from this discussion.

hedipaldi
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Hi,
Using the definition of Hausdorff measure:
http://en.wikipedia.org/wiki/Hausdorff_measure
I am looking for a simple proof that Hd(C) is greater than 0, where C is the Cantor set and
d=log(2)/log(3)
Thank's in advance
 
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