Dear all,


I have recently found the following discussion:
[Different Measures On R2](https://mathoverflow.net/questions/102061/hausdorff-measure-and-minkowskis-content-boundary-measures) 
regarding different boundary measures on $\mathbb{R}^n $ . 


The discussion made me wondering:


Is there any example in the opposite direction?


i.e. an example of a set $A \subseteq \mathbb{R} ^n $ such that $ Leb^+ (A) > H^{n-1} (\partial A) $ ? 


Thanks in advance ! 



Geometric Measure Theory On Euclidean Spaces
Take $[0,1]\times \{0\} \subset \mathbb{R}^2$.


