A class of functions is a Donsker class of the empirical process (see empirical process theory) given by obeys a CLT. (Note that they are CLTs in function classes, i.e., the uniform metric). Donsker classes are similar to GC classes, but for convergence in distribution instead of convergence in probability or almost sure convergence. Typically the empirical process will converges to a Gaussian process, but in theory it could be any infinitely divisible distribution.
If a class has a finite entropy integral (see Dudley’s entropy bound) in terms of covering numbers, then it is Donsker. If it has finite VC dimension (see Vapnik-Chervonenkis theory) it is often Donsker.