On the equivalence of integral norms on the space of measurable polynomials witj respect to a convex measure

We prove that, for a convex product-measure $\mu$ on a locally convex space, for any set $A$ of positive measure, on the space of measurable polynomials of degree $d,$ all $L_p(\mu)$-norms coincide with the norms obtained by restricting $\mu$ to $A.$