  The paper is devoted to discretization of integral norms of functions from a
given finite dimensional subspace. Even though this problem is extremely
important in applications, its systematic study has begun recently. In this
paper we obtain a conditional theorem for all integral norms $L_q$, $1\le
q<\infty$, which is an extension of known results for $q=1$. To discretize the
integral norms successfully, we introduce a new technique, which is a
combination of probabilistic technique with results on the entropy numbers in
the uniform norm. As an application of the general conditional theorem, we
derive a new Marcinkiewicz type discretization for the multivariate
trigonometric polynomials with frequencies from the hyperbolic crosses.
