  We provide an affirmative answer to the question posed in the title. Our
argument is based on a treatment of the Schroedinger dynamics of the composite
of a quantum microsystem, S, and a macroscopic measuring apparatus, I,
consisting of N interacting particles. The pointer positions of this apparatus
are represented by orthogonal subspaces of its representative Hilbert space
that are simultaneous eigenspaces of coarse-grained macroscopic observables. By
taking explicit account of their macroscopicality via a large deviation
principle, we prove that, for a suitably designed apparatus I, the evolution of
the composite (S+I) leads both to the reduction of the wave packet of S and to
a one-to-one correspondence between the resultant state of this microsystem and
the pointer position of I, up to utterly negligible corrections that decrease
exponentially with N.
