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).

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.)

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).

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.)