Operational weak and strong secrecy capacities

Fix an error criterion $e\in \{\mathrm{a}\mathrm{v},\mathrm{m}\mathrm{a}\mathrm{x}\}$ and a secrecy criterion $s\in \{\mathrm{w}\mathrm{e}\mathrm{a}\mathrm{k},\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{g}\}$. For each code let $P_{\mathrm{e}\mathrm{r}\mathrm{r}}^{(n)}=P_{e,\mathrm{a}\mathrm{v}}^{(n)}$ when $e=\mathrm{a}\mathrm{v}$ and $P_{\mathrm{e}\mathrm{r}\mathrm{r}}^{(n)}=P_{e,\mathrm{m}\mathrm{a}\mathrm{x}}^{(n)}$ when $e=\mathrm{m}\mathrm{a}\mathrm{x}$. A rate $R\ge 0$ in nats per channel use is $(e,s)$-achievable for a finite wiretap channel Finite discrete memoryless wiretap channel and code model if there is a sequence of wiretap codes, one at each blocklength $n\ge 1$, such that

${\mathrm{lim\hspace{0.17em}inf}}_{n\to \mathrm{\infty }}\frac{1}{n}\ln \mathrm{\mid }{\mathcal{M}}_n\mathrm{\mid }\ge R,P_{\mathrm{e}\mathrm{r}\mathrm{r}}^{(n)}⟶0,$

and the sequence satisfies secrecy criterion $s$ from Weak and strong secrecy for wiretap code sequences, with leakage measured by Information leakage and equivocation for finite observations. Define $C_{e,s}$ as the supremum of all such rates. Thus this definition gives four operational capacities, distinguished by average or maximal error and weak or strong secrecy.