  We introduce contextual values as a generalization of the eigenvalues of an
observable that takes into account both the system observable and a general
measurement procedure. This technique leads to a natural definition of a
general conditioned average that converges uniquely to the quantum weak value
in the minimal disturbance limit. As such, we address the controversy in the
literature regarding the theoretical consistency of the quantum weak value by
providing a more general theoretical framework and giving several examples of
how that framework relates to existing experimental and theoretical results.
