Hausdorff dimension of the Cantor Set

alpar_r

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?

g_edgar

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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alpar_r	Hausdorff dimension of the Cantor Set Tweet 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?

g_edgar	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!