Vacuum States and Equidistribution of the Random Sequence for Glimm's Scheme (continuation)

This is a continuation of paper 1]. The difference between this paper and paper 1] is that the initial functions considered here are step functions and those considered in 1] are. Lipschitz continuous. Since there are centered rarefaction waves here, more delicate techniques are needed. It may be a necessary step in solving p-System with general initial functions by Glimm's scheme. Notice that this paper can not be deduced from 1].