According to Bohr, the definition of the almost periodic function is: A function $f:\mathbb{R}\rightarrow \mathbb{C}$ is called almost periodic if it is continuous and if for every positive $\epsilon$, there exists a positive number $l$ such that every closed interval of length $l$ contains an $\epsilon$-almost period.

Intuitively, when $\epsilon$ is getting smaller, the corresponding $l$ is getting larger. But is this always correct? If it is correct, may I ask how to prove it? Also, is there any relation between $\epsilon$ and the corresponding $\epsilon$-almost period?