Decision Procedures in Quantum Mechanics

The results of an earlier paper on finite and infinite sequences of measurements are here extended to include decision procedures. It is shown that with each decision procedure Q there is uniquely associated a probability operator measure OQ, which gives the statistical properties of Q. None, some, or all of the paths of Q can be infinitely long. A result of this association is that there are two methods of measuring the probability that carrying out Q on a system in state ρ gives an outcome sequence in some set F. A remarkable aspect of this equivalence is that the purely physical operation of one method is equivalent to, or can replace, the physical operation and mathematical decision procedure of the other method.