Entropy of Endomorphisms and Relative Entropy in Finite von Neumann Algebras

We show the analogue for the entropy of automorphisms of finite von Neumann algebras of the classical formula H(T)=H(∨∞i=0 T−iP ∣ ∨∞i=1 T−iP), where T is a measure preserving transformation of a probability space, and P is a generator.