Is there any co-area formula involving non-integer Hausdorff dimension?
Moreover is it sensible to write the following:
Let $S$ be a subset in $ \mathbb{R}^n$ with Hausdorff dimension s $(0
$ \int_{S_\epsilon} dy = \int_S \int_{B(x,\epsilon)} \; dy \; d\mu(x)$ where $ \mu $ is a uniformly $s$-dimensional measure.