Consider the Cauchy problem for a hyperbolic n x n system of conservation l
aws in one space dimension:
u(t) + f(u)(x) = 0, u(0, x) = (u) over bar(x). (CP)
Relying on the existence of a continuous semigroup of solutions, we prove t
hat the entropy admissible solution of (CP) is unique within the class of f
unctions u = u(t, x) which have bounded variation along a suitable family o
f space-like curves.