Corollary

A sequence of Shannon-Fano (or arithmetic) codes $\{ \mathcal{C}_{n} \}$ obtained from a sequence of coding distributions $\{ q_{n} \}$ is universal for a source class $\mathcal{P}$ if and only if $$\lim_{ n \to \infty } \frac{1}{n}D(p\|q_{n})=0, \ \ \forall p\in\mathcal{P}$$