  To a sequence (s_n)_{n\ge 0} of real numbers we associate the sequence of
Hankel matrices \mathcal H_n=(s_{i+j}),0\le i,j \le n. We prove that if the
corresponding sequence of Hankel determinants D_n=\det\mathcal H_n satisfy
D_n>0 for n<n_0 while D_n=0 for n\ge n_0, then all Hankel matrices are positive
semi-definite, and in particular (s_n) is the sequence of moments of a discrete
measure concentrated in n_0 points on the real line. We stress that the
conditions D_n\ge 0 for all n do not imply the positive semi-definiteness of
the Hankel matrices.
