  A Sidon set is a set A of integers such that no integer has two essentially
distinct representations as the sum of two elements of A. More generally, for
every positive integer g, a B_2[g]-set is a set A of integers such that no
integer has more than g essentially distinct representations as the sum of two
elements of A. It is proved that almost all small sumsets of {1,2,...,n} are
B_2[g]-sets, in the sense that if B_2[g](k,n) denotes the number of B_2[g]-sets
of cardinality k contained in the interval {1,2,...,n}, then lim_{n\to\infty}
B_2[g](k,n)/\binom{n}{k} = 1 if k = o(n^{g/(2g+2)}).
