It is not correct— at least not unless you subscribe to the Copenhagen interpretation. Yet, while this interpretation is a simple heuristic for interaction with big systems (e.g., a photon hits a CCD array), none of the quantum physicists I know treat it seriously (for that matter, I have a PhD in quantum optics theory).
I mean, at some certain level, everything is "just a mathematical representation" - in the spirit of "all models are wrong but some are useful". But the wavefunction is more fundamental than measurement. The other can be thought of as a particle entangling with a system so large that, for statistical reasons, it becomes irreversible - because of chaos, not fundamental rules.
For some materials, I recommend materials on decoherence by WH Zurek, e.g. https://arxiv.org/pdf/quant-ph/0105127. Some other references (here a shameless self ad) in https://www.spiedigitallibrary.org/journals/optical-engineer... - mostly in the introduction and, speaking about interpretations, section 3.7.
EDIT: or actually even simpler toy model of measurement, look at the Schrodinger cat in this one: https://arxiv.org/abs/2312.07840