  We discuss the case of a Markovian master equation for an open system, as it
is frequently found from environmental decoherence. We prove two theorems for
the evolution of the quantum state. The first one states that for a generic
initial state the corresponding Wigner function becomes strictly positive after
a finite time has elapsed. The second one states that also the P-function
becomes exactly positive after a decoherence time of the same order. Therefore
the density matrix becomes exactly decomposable into a mixture of Gaussian
pointer states.
