# Singularity spectrum

More formally, the singularity spectrum $D(\alpha)$ of a function, $f(x)$, is defined as:
$D(\alpha) = D_F\{x, \alpha(x) = \alpha\}$
Where $\alpha(x)$ is the function describing the Holder exponent, $\alpha(x)$ of $f(x)$ at the point $x$. $D_F\{\cdot\}$ is the Hausdorff dimension of a point set.