The result below is originally due to Day when $H$ is a locally compact group
Theorm Let $H$ be a locally compact group, $H$ is amenable if and only if there is a net $\{f_\alpha\}_\alpha \subset L^1(H) $ such that for every $x\in H$ $$\|f_\alpha-\delta_x*f_\alpha\|\to 0$$
I don't find the original paper
Could anyone please suggest me how to deal with these questions?