  We provide a numerical scheme to approximate as closely as desired the
Gaussian or exponential measure $\mu(\om)$ of (not necessarily compact) basic
semi-algebraic sets$\om\subset\R^n$. We obtain two monotone (non increasing and
non decreasing) sequences of upper and lower bounds $(\overline{\omega}\_d)$,
$(\underline{\omega}\_d)$, $d\in\N$, each converging to $\mu(\om)$ as
$d\to\infty$. For each $d$, computing $\overline{\omega}\_d$ or
$\underline{\omega}\_d$reduces to solving a semidefinite program whose size
increases with $d$. Some preliminary (small dimension) computational
experiments are encouraging and illustrate thepotential of the method. The
method also works for any measure whose moments are known and which satisfies
Carleman's condition.
