  This paper discusses the relation between the decoherent histories approach
to quantum mechanics that is based on coarse-grained decoherent histories of a
closed system, and the approximate quantum mechanics of measured subsystems, as
in the Copenhagen interpretation. We show how the a classical world used in
such formulations is not to something to be postulated but rather explained by
suitable sets of alternative histories of quasiclassical variables. We discuss
the general definition of measurement, the collapse of the wave function, and
irreversibility from the perspective of decoherent histories quantum theory..
