What's the best place to read a proof of the full-generality Fisher Neyman factorisation theorem? I have a few stats books that claim to give a proof but they leave out steps like, for instance, why a dominated family of distributions is equivalent to the mixture of a countable subfamily -- and they're just generally irritating for other reasons.
2026-04-01 01:11:10.1775005870
Fisher Neyman factorisation theorem
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Not a bad question. A paper by Halmos and Savage claimed to do this, and I heard there was a gap in the argument, consisting of a failure to prove certain sets have measure zero:
I've heard the the first fully sound proof was by R. R. Bahadur, but I'm not succeeding in finding that right now.
It's easy to prove in the discrete case.