  It is demonstrated that the collapse of the wave function is equivalent to
the continuity of measurement outcomes. The latter states that a second
measurement has to result in the same outcome as the first measurement of the
same observable for a vanishing time between both observations. In contrast to
the exclusively quantum-physical collapse description, the equivalent
continuity requirement also applies in classical physics, allowing for a
comparison of both domains. In particular, it is found that quantum coherences
are the single cause for measurable deviations in statistical properties due to
the collapse. Therefore, the introduced approach renders it possible to
characterize and quantify the unique features of the quantum-physical
measurement problem within the framework of modern quantum resource theories
and compare them to classical physics.
