## LESSWRONGLW

Yes I'm quite aware... note that if there's a sequence of outcomes whose values increase without bound, then you could construct a lottery that has infinite value by appropriately mixing the lotteries together, e.g. put probability 2^-k on the outcome with value 2^k. Then this lottery would be problematic from the perspective of continuity (or even having an evaluable utliity function).

[anonymous]6y0

Are lotteries allowed to have infinitely many possible outcomes? (The Wikipedia page about the VNM axioms only says "many"; I might look it up on the original paper when I have time.)