1. But an inspection of the proof shows that we really only need A3 to hold on SmpRegpN, X q. (b) Heuristically, the proof of the theorem involves three steps: 1. Show that ? has an additive utility representation or SEU representation involving a finitely additive;a) I have required Axiom A3 (Separability) to apply on all of RegpN, X q
2. But I could also have used any other axiomatic characterization of subjective expected utility. 20 As already noted, one complication is that B is not a Boolean algebra;Step 1, I used Axioms A1 -A4 and the proof strategy of Wakker and Zank,1999