Fair point. And while it's too late to edit my post, I think I found the flaw in the math. Just because X converges in probability to x, f(X) doesn't necessari

Fair point. And while it's too late to edit my post, I think I found the flaw in the math. Just because X converges in probability to x, f(X) doesn't necessarily converge in probability to f(x). If that were so, then logarithmic utility would be sound, but it isn't.