  Measurement is a fundamental notion in the usual approximate quantum
mechanics of measured subsystems. Probabilities are predicted for the outcomes
of measurements. State vectors evolve unitarily in between measurements and by
reduction of the state vector at measurements. Probabilities are computed by
summing the squares of amplitudes over alternatives which could have been
measured but weren't. Measurements are limited by uncertainty principles and by
other restrictions arising from the principles of quantum mechanics. This essay
examines the extent to which those features of the quantum mechanics of
measured subsystems that are explicitly tied to measurement situations are
incorporated or modified in the more general quantum mechanics of closed
systems in which measurement is not a fundamental notion. There, probabilities
are predicted for decohering sets of alternative time histories of the closed
system, whether or not they represent a measurement situation. Reduction of the
state vector is a necessary part of the description of such histories.
Uncertainty principles limit the possible alternatives at one time from which
histories may be constructed. Models of measurement situations are exhibited
within the quantum mechanics of the closed system containing both measured
subsystem and measuring apparatus. Limitations are derived on the existence of
records for the outcomes of measurements when the initial density matrix of the
closed system is highly impure. (Festschrift for Dieter Brill).
