Procedures in Quantum Mechanics without Von Neumann's Projection Axiom

The results of previous work are generalized to include procedures whose measurement operations correspond to expectations as defined by Davies. For such procedures Von Neumann's projection axiom is not in general applicable. Finite and infinite sequences of measurements and transformations as well as finite and infinite decision procedures are considered. It is shown that with each such procedure there is associated in a unique manner a probability operator measure.