  In 1997 H.G.Diamond gave a condition on Beurling's generalized prime numbers
in order that the corresponding generalized integers have a density. We give a
new proof of this condition (Theorem 1) and a proof that it is not necessary
(Theorem 2 and Examples). However, it is very near to be necessary (Theorem 3).
Both proofs of Theorems 1 and 2 rely on Fourier analysis, mainly the Wiener
algebra, and partly on probability methods.
