In the case of a scalar conservation law with convex flux in space dimension one, P. D. Lax proved [Comm. Pure and Appl. Math. 7 (1954)] that the semigroup defining the entropy solution is compact in L for each positive time. The present note gives an estimate of the -entropy in L of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L1. © 2005 Wiley Periodicals, Inc.