Hausdorff dimension of the Cantor Set


by alpar_r
Tags: cantor, dimension, hausdorff
alpar_r
alpar_r is offline
#1
Nov16-10, 06:19 PM
P: 1
Hi everyone!

I am thinking about, how can calculate the Hausdorff dimension of the Cantor set? I know, that this dimension is [tex]\frac{\log 2}{\log 3}[/tex] but I cannot prove it.

Any ideas?
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g_edgar
g_edgar is offline
#2
Nov17-10, 09:21 AM
P: 608
Of course you will need to use the definition of Hausdorff dimension. In one popular proof, you do it in two parts: One shows the dimension is <= log 2/log 3 and the other shows the dimension is >= log 2/log 3 . But of course both of them need the definition!


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