International audienceConsider the sub-level set K := {x : g(x) ≤ 1} of a nonnegative homogeneous polynomial g. We show that its Lebesgue volume vol(K) can be approximated as closely as desired by solving a sequence of generalized eigenvalue problems with respect to a pair of Hankel matrices of increasing size, whose entries are obtained in closed form. An extension to the non-homogeneous case is also briefly described