I have a domain $X$ and a set system $R$ on $X$, such that the sets in $R$ are one included in the other, that is, for any $A,B\in R$, either $A\subseteq B$ or $B\subseteq A$. The sets are not all equal: there is at least a pair of sets $A,B\in R$ such that $A\subsetneq B$ The VC-dimension for this set is therefore 1.
I seem to recall that the usual random sampling theorem to obtain an $(\varepsilon,\delta)$ approximation of the sizes of all the sets in $R$ can be used only if the range space has VC-dimension at least 2, but now I cannot find this explicitly stated anywhere. Could anyone please tell me whether I am just remembering it wrong and the theorem can be used for range spaces of any VC-dimension?
If not, are there other techniques I can use or do I have to resort to Chernoff+union bounds?