Uniform convergence for a class of finite dimension
The keyword to look for is Dudley's chaining integral, see e.g. Vershynin's book &quot;High Dimensional Probability&quot; which contains a chapter on the chaining technique. Chaining allows us to bound the empirical Rademacher complexity in terms of the empirical $L_2$ covering numbers of $\mathcal{A}$. Your result is directly obtained from the chaining integral and a result (which is think is credited to Dudley-Pollard) which relates the $L_1$ covering numbers (irrespective of the distribution) to the pseudo dimension, see e.g. theorem 4.2 in these notes. You still need to go from $L_2$ covering to $L_1$ somehow, this is easy when the functions are binary valued.