  We study the relationship between POV-measures in quantum theory and
asymptotic morphisms in the operator algebra E-theory of Connes-Higson. This is
done by introducing the theory of "asymptotic" PV-measures and their integral
correspondence with positive asymptotic morphisms on locally compact spaces.
Examples and applications involving various aspects of quantum physics,
including quantum noise models, semiclassical limits, strong deformation
quantizations, and pure half-spin particles, are also discussed.
