  This short note gives a sufficient condition for having the class of
polynomials dense in the space of square integrable functions with respect to a
finite measure dominated by the Lebesgue measure in the real line, here denoted
by $L^2$. It is shown that if the Laplace transform of the measure in play is
bounded in a neighbourhood of the origin, then the moments of all order are
finite and the class of polynomials is dense in $L^2$. The existence of the
moments of all orders is well known for the case where the measure is
concentrated in the positive real line (see Feller, 1966), but the result
concerning the polynomial approximation is original, even thought the proof is
relatively simple. Additionally, an alternative stronger condition easier to be
verified not involving the calculation of the Laplace transform is given. The
condition essentially says that the density of the measure should have
exponential decaying tails. The tools presented are of interest for
constructing semiparametric extensions of classic parametric models.
