Lebesgue decomposition in action via semidefinite relaxations

Given all (finite) moments of two measures $mu$ and $lambda$ on $R^n$, we provide a numerical scheme to obtain the Lebesgue decomposition $mu= u+psi$ with $ ulllambda$ and $psiperplambda$. When$ u$ has a density in $L_infty(lambda)$ then we obtain two sequences of finite moments vectorsof increasing size (the number of moments) which converge to the moments of $ u$ and $psi$ respectively, as the number of moments increases. Importantly, {it no} `a priori knowledge on the supports of $mu, u$ and $psi$ is required.