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Stochastic Schrödinger equations describing the time evolution of a subsystem in contact with its environment can be deduced from the Schrödinger equation of the total system. The wavefunction ruled by a stochastic Schrödinger equation may undergo a localization during its time evolution, which is here shown to correspond to the localization of subsystem-environment observables. Such localizations are randomly distributed according to the subsystem density matrix, in particular, when this latter becomes diagonal after relaxation, suggesting an understanding of the randomness which manifests itself during quantum measurement. |