On the entropy in Hi von Neumann algebras

. Let a be an automorphism of a finite von Neumann algebra and let H(a) be its Connes-St0rmer's entropy. We show that H[a) = O if a is the induced automorphism on the crossed product of a Lebesgue space by a pure point spectrum transformation. We also show that H is not continuous in a and we compute H(a) for some a.