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Supmech, the universal mechanics developed in the previous two papers,accommodates both quantum and classical mechanics as subdisciplines (a briefoutline is included for completeness); this feature facilitates, in a supmechbased treatment of quantum measurements, an unambiguous treatment of theapparatus as a quantum system approximated well by a classical one. Takingexplicitly into consideration the fact that observations on the apparatus aremade when it has `settled down after the measurement interaction' and arerestricted to macroscopically distinguishable pointer readings, the unwantedsuperpositions of (system + apparatus) states are shown to be suppressed; thisprovides a genuinely physics based justification for the (traditionally\emph{postulated}) von Neumann projection/collapse rule. The decoherencemechanism brought into play by the stated observational constraints is freefrom the objections against the traditional decoherence program.

A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. III : Measurements and von Neumann Projection/Collapse Rule