I'd like to show that the Haussdorf-Dimension of the Cantor set is log(2)/log(3).

Although I have some Ideas how to do this, I'm not sure if any of it is correct. A little guidance would be greatly appreciated. I hope you guys are familiar with the terms I use. Otherwise I refer to Hausdorff measure - Wikipedia, the free encyclopedia

My idea was to make an upperbound for

Starting with .

Here is the total length of and the maximum diameter of a Cover-element of .

Now we need to find out for which this upperbound exists, if we let and .

How to do this, I'm not sure yet.

Can anyone help me in the right direction?