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Concepts, familiar from pure states in quantum mechanics, such as "superposition" and "transition probability", are shown to be also meaningful for generic states in infinite systems, described by funnels of type I_{\infty} algebras. In the physically important case of states of Connes-von Neumann type III1, these concepts also have a physically significant operational interpretation in terms of primitive observables. (Joint work with Erling Störmer)