Let $\tau_1,\tau_2 $ be topologies on group $G$ such that $(G,\tau_1),(G,\tau_2)$ be a locally compact group. Let $\tau_1\subseteq\tau_2$ and $(G,\tau_2)$ be an amenable group, when $(G,\tau_1)$ is amenable?
(Particularly, let $\tau_2 $ be the discrete topology on $G$, then $l^1(G)$ be amenable. When $L^1(G,\tau_1)$ is amenable?)