Title: On Diamond's $L^1$ criterion for asymptotic density of Beurling generalized integers,
Abstract: We give a short proof of the $L^{1}$ criterion for Beurling generalized
integers to have a positive asymptotic density. We actually prove the existence
of density under a weaker hypothesis. We also discuss related sufficient
conditions for the estimate $m(x)=\sum_{n_{k}\leq x} \mu(n_k)/n_k=o(1)$, with
$\mu$ the Beurling analog of the Moebius function.