  We present a complex probability measure relevant for double (pairs of)
states in quantum mechanics, as an extension of the standard probability
measure for single states that underlies Born's statistical rule. When the
double states are treated as the initial and final states of a quantum process,
we find that Aharonov's weak value, which has acquired a renewed interest as a
novel observable quantity inherent in the process, arises as an expectation
value associated with the probability measure. Despite being complex, our
measure admits the physical interpretation as mixed processes, i.e., an
ensemble of processes superposed with classical probabilities.
