Why Are the Definitions of Hausdorff Dimension Equivalent?

[hedipaldi]

Hi,
I am trying to understand why do the two versions of Hausdorff (fractal) dimension are actually the same.I refer to the definition by coverings and the definition by ratio of two logarythms.

http://en.wikipedia.org/wiki/Hausdorff_measure
http://www.math.umass.edu/~mconnors/fractal/sierp/sierp.html

Thank's in advance

 

[HallsofIvy]

These are NOT two "versions" of the Hausdorff dimension. The first is the (Wkipedia) definition, the second is an example of calculating it in a particular case. The definition deals with covering the (fractal) set by sets with integer dimension and the triangles in the example are precisely that.