The vNM argument only uses preference over lotteries with finitely many possible outcomes to assign utilities to pure outcomes. One can use measure theory arguments to pin down the expected utilities of other lotteries. That some lotteries have infinite value does not seem to me to be a big problem.
The vNM argument only uses preference over lotteries with finitely many possible outcomes to assign utilities to pure outcomes. One can use measure theory arguments to pin down the expected utilities of other lotteries. That some lotteries have infinite value does not seem to me to be a big problem.