  In the eighties, A. Connes and E. J. Woods made a connection between
hyperfinite von Neumann algebras and Poisson boundaries of time dependent
random walks. The present paper explains this connection and gives a detailed
proof of two theorems quoted there: the construction of a large class of states
on a hyperfinite von Neumann algebra (due to A. Connes) and the ergodic
decomposition of a Markov measure via harmonic functions (a classical result in
probability theory). The crux of the first theorem is a model for conditional
expectations on finite dimensional C*-algebras. The proof of the second theorem
hinges on the notion of cotransition probability.
