# nLab Hausdorff dimension

Hausdorff dimension is a method of measuring the dimension of a metric space. It is always a non-negative real number, but it need not be an integer; one way to define a fractal? is a metric space with a fractional (non-integral) Hausdorff dimension.

The Hausdorff dimension of the cartesian space $\mathbb{R}^n$ (or any inhabited open subset thereof) is $n$. The Hausdorff dimension of a self-similar fractal which consists of $n$ copies of itself reduced in size by a factor of $m$ is $\log_m n$.

In general, Hausdorff dimension may be defined using Hausdorff measure?. See Wikipedia.

Revised on May 30, 2010 23:36:01 by Toby Bartels (75.88.94.122)