All you’ve shown is that maximizing expected utility infinitely many times does not maximize the expected utility you get at the end of the infinitely many decisions you’ve made. This is entirely a matter of switching a limit and an integral, and it is irrelevant to practical decision-making.
All you’ve shown is that maximizing expected utility infinitely many times does not maximize the expected utility you get at the end of the infinitely many decisions you’ve made. This is entirely a matter of switching a limit and an integral, and it is irrelevant to practical decision-making.