$\sigma$-additivity - probability of a sum of countable number of pairly disjoint events equals a sum of probabilities of these events.

Since there are different methods of summing amplitudes in QM depending on whether outcomes of measurement are distinguishable or not (i.e. in case of identical particles and non-identical particles [Feynman vol. 3]), does it mean that "probability" in QM does not satisfy the $\sigma$-additivity which is crucial property in classical probability?