Hausdorff dimension
The new approach of the notion of dimension can be defined rigorously. Given two real numbers and , one can overlap the studied set by sphere of diameter , all lower that (see the figure), then one calculate the limit :
The limit when tends to 0 of the minorant, corresponds to all spheres of the sum of power of
One can show there exist one value of such as:
has a finite value for .
is the Hausdorff dimension of the set .