Operator valued weights in von Neumann algebras,I

An operator valued weight is a kind of generalized conditional expectation from a von Neumann algebra M to a sub von Neumann algebra N. If T is a n.f.s. (normal, faithful, semifinite) operator valued weight from M to N, and φ is a n.f.s. weight on N, then φ ° T defines a n.f.s. weight on M. Our main result is that σ_t^φ°T extends σ_t^φ, and that the map φ → φ ° T preserves cocycle Radon Nikodym derivatives.