  We propose a theory of quantum (statistical) measurement which is close, in
spirit, to Hepp's theory, which is centered on the concepts of decoherence and
macroscopic (classical) observables, and apply it to a model of the
Stern-Gerlach experiment. The number N of degrees of freedom of the measuring
apparatus is such that $N \to \infty$, justifying the adjective "statistical",
but, in addition, and in contrast to Hepp's approach, we make a three-fold
assumption: the measurement is not instantaneous, it lasts a finite amount of
time and is, up to arbitrary accuracy, performed in a finite region of space,
in agreement with the additional axioms proposed by Basdevant and Dalibard. It
is then shown how von Neumann's "collapse postulate" may be avoided by a
mathematically precise formulation of an argument of Gottfried, and, at the
same time, Heisenbeg's "destruction of knowledge" paradox is eliminated. The
fact that no irreversibility is attached to the process of measurement is shown
to follow from the author's theory of irreversibility, formulated in terms of
the mean entropy, due to the latter's property of affinity.
