Dear all,

Is there any possible way to construct a set $A \subseteq \mathbb{R}^n $ for which $ H^{n-1} (\partial A) > Leb^ + (A ) $?

Where $ H^{n-1} (\partial A) $ is the Hausdorff measure of the boundary of $A$ and: $ Leb^{+} (A) = \lim_{\epsilon \to 0 } \frac{ Leb(A_ \epsilon) - Leb(A) }{\epsilon} $ , $A_\epsilon := \{ x \in \mathbb{R} ^n | d(x,A) \leq \epsilon \} $ =Minkowski's content with respect to Lebesgue measure.

Thanks in advance !