PAC-learning bound with epsilon-cover of hypothesis class
This follows from Massart's finite class lemma. Let $F$ is a binary function class restricted to some set $\{X_1,\ldots,X_n\}$, and let $P_n$ be the empirical (i.e., uniform) measure on this set. Then, for any $\epsilon&gt;0$, the empirical Rademacher complexity of $F$ is bounded by
$$ R_n(F;X) \le \epsilon + \sqrt{\frac{2\log N_F(\epsilon)}{n}},$$
where $N_F(\epsilon)$ is the $\ell_2$ $\epsilon$-covering number of $F$ w.r.t. $P_n$. This is proved in display (1) here:
https://www.cs.bgu.ac.il/~asml162/wiki.files/dudley-pollard.pdf
-- check out the course notes:
https://www.cs.bgu.ac.il/~asml162/Class_Material