  Given two measures $\mu$, $\nu$ on Rd that satisfy Carleman's condition, we
provide a numerical scheme to approximate as closely as desired the total
variation distance between $\mu$ and $\nu$. It consists of solving a sequence
(hierarchy) of convex relaxations whose associated sequence of optimal values
converges to the total variation distance, an additional illustration of the
versatility of the Moment-SOS hierarchy. Indeed each relaxation in the
hierarchy is a semidefinite program whose size increases with the number of
involved moments. It has an optimal solution which is a couple of degree-2n
pseudo-moments which converge, as n grows, to moments of the Hahn-Jordan
decomposition of $\mu$-$\nu$.
