The redundancy of a prefix $n$-code $\mathcal{C}_{n}:\mathcal{X}\to \{ 0,1 \}^{*}$ w.r.t. the source distribution $p\in\mathcal{P}$ is $$\begin{align*} R(\mathcal{C}_{n},p)&= \bar{R}_{n}(\mathscr{l}(\mathcal{C}_{x^{n}}))- \frac{1}{n}H_{p}(X^{n})\\ &=\frac{1}{n}[E_{p}[\mathscr{l}(\mathcal{C}_{x^{n}})]-H_{p}(X^{n})] \end{align*}$$