Let $0<h, r\in \mathbb{R}$ be given and let $V\subseteq \mathcal{R}^k$ be the point $u, v\in\mathbb{R}^k$ such that $2h<||u-v||\leq r$. In my reseach, I need to find cardinality of $B(u, s)\cap V$.
Indeed, let $u\in\mathbb{R}^k$ and $s>0$ be given. In a paper, Author claim that \begin{equation} |B(u, s)\cap V|\leq (1+\frac{s}{h})^k \end{equation} but it is not clear for me. Please help me to know it. In the case of $k=1$, proof is clear.