Let $A$ be a $k$-dimensional rectangle in $\mathbb{R}^k$.
Then $\displaystyle H_p(A)=\sup_{n\in N}H_{p,1/n}(A) \geq \inf_{n \in N}H_{p,1/n}(A)$
How can I find an example (A) such that $H_p(A) > \inf_{n \in N}H_{p,1/n}(A)$
Let $A$ be a $k$-dimensional rectangle in $\mathbb{R}^k$.
Then $\displaystyle H_p(A)=\sup_{n\in N}H_{p,1/n}(A) \geq \inf_{n \in N}H_{p,1/n}(A)$
How can I find an example (A) such that $H_p(A) > \inf_{n \in N}H_{p,1/n}(A)$