One possibility is this: I don’t value prospects by their classical expected utilities, but by the version calculated with the hyperreal sum or integral (which agrees to within an infinitesimal when the answer is finite, but can disagree when it is divergent). So I don’t actually want the classical expected utility to be the measure of a prospect. It is possible that the continuity axiom gets you there and my modified or dropped version can allow caring about the hyperreal version of expectation.
One possibility is this: I don’t value prospects by their classical expected utilities, but by the version calculated with the hyperreal sum or integral (which agrees to within an infinitesimal when the answer is finite, but can disagree when it is divergent). So I don’t actually want the classical expected utility to be the measure of a prospect. It is possible that the continuity axiom gets you there and my modified or dropped version can allow caring about the hyperreal version of expectation.