Proof of Pitman–Koopman–Darmois theorem

Where can I find a proof of Pitman–Koopman–Darmois theorem? I have googled for quite some time. Strangely, many notes mention this theorem yet none of them present the proof.

The proof is somewhat technical and can be found in its original form here:

On Distributions Admitting a Sufficient Statistic -- Koopman: http://yaroslavvb.com/papers/koopman-on.pdf