## LESSWRONGLW

[anonymous]6y2

(and I think [a bounded utility function] is even necessary if you want to satisfy the VNM axioms, otherwise you violate the continuity axiom)

An unbounded function is one that can take arbitrarily large finite values, not necessarily one that actually evaluates to infinity somewhere.

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).