  R. P. Boas showed that any single-index sequence $\left\{ \beta_i
\right\}_{i=0}^\infty$ of real numbers can be represented as $\beta_i
=\int_0^\infty x^i \, d\mu$ ($i=0,1,2,\ldots$), where $\mu$ is a signed
measure. As Boas said his observation seemed to be quite unexpected; however,
it is even possible to extend the result to any multi-index sequence of real
numbers. In addition, we can also prove that any multi-index finite sequence
admits a measure of a similar type.
