  Let $\tau$ be a locally convex topology on the countable dimensional
polynomial $\reals$-algebra $\rx:=\reals[X_1,...,X_n]$. Let $K$ be a closed
subset of $\reals^n$, and let $M:=M_{\{g_1, ... g_s\}}$ be a finitely generated
quadratic module in $\rx$. We investigate the following question: When is the
cone $\Pos(K)$ (of polynomials nonnegative on $K$) included in the closure of
$M$? We give an interpretation of this inclusion with respect to representing
continuous linear functionals by measures. We discuss several examples; we
compute the closure of $M=\sos$ with respect to weighted norm-$p$ topologies.
We show that this closure coincides with the cone $\Pos(K)$ where $K$ is a
certain convex compact polyhedron.
