# Co-area formula involving non-integer Hausdorff measure

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 $(0<s<n)$ and $S_\epsilon = \bigcup_{x \in S}B(x,\epsilon)$.

$\int_{S_\epsilon} dy = \int_S \int_{B(x,\epsilon)} \; dy \; d\mu(x)$ where $\mu$ is a uniformly $s$-dimensional measure.

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