  We show that for every positive p, the L_p-norm of linear combinations (with
scalar or vector coefficients) of products of i.i.d. random variables, whose
moduli have a nondegenerate distribution with the p-norm one, is comparable to
the l_p-norm of the coefficients and the constants are explicit. As a result
the same holds for linear combinations of Riesz products.
  We also establish the upper and lower bounds of the L_p-moments of partial
sums of perpetuities.
