  Let $\mu^z$ be the measure obtained by sweeping out the Monge-Amp\`ere
measure of the pluricomplex Green function with pole at $z. $ We prove that
$\mu^z$ vanish on Levi flat parts of the boundary for 1) every relatively
compact analytic polyhedron in complex space, 2) product domains of hyperconvex
sets in Stein manifolds.
