Dear all,

I have recently found the following discussion: Different Measures On R2 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 !