Let M denote a σ-compact locally compact metric space which satisfies certain geometrical conditions. Then for each σ-additive projection valued measure P on M there can be constructed a canonical Radon-Nikodym derivative Π:α↦πα, α∈M, with respect to a suitable basic measure ρon M. The family (Πα)α∈M consists of generalized eigenprojections related to the commutative von Neumann algebra generated by the projections P(Δ), Δ a Borel set of M