  Given a bounded class of functions G and independent random variables X1, . .
. , Xn, we provide an upper bound for the expectation of the supremum of the
empirical process over elements of G having a small variance. Our bound applies
in the cases where G is a VC-subgraph or a VC-major class and it is of smaller
order than those one could get by using a universal entropy bound over the
whole class G . It also involves explicit constants and does not require the
knowledge of the entropy of G
