The Glivenko-Cantelli Theorem (Wikipedia) states that for $X_1,\ldots,X_n$ with common c.d.f. $F$, $$\|F_n-F\|_\infty = \sup|F_n(x)-F(x)|\stackrel{a.s.}{\to}0,$$ where $F_n$ is the empirical c.d.f. for a sample size $n$.
Slide 2 of Bartlett's lecture notes state that this theorem is an example of a uniform law of large numbers (ULLN). This implies that there are other ULLNs. Is this understanding correct?
Additionally, slide 5 in the same notes states that the Glivenk-Cantelli Theorem is a special case of the Glivenko-Cantelli class. Is the Glivenko-Cantelli class a broader ULLN than the theorem? Obviously, a set of functions which is a GC class follows ULLN. Does following ULLN also imply that a function is a GC class?