A system which selects actions so as to maximize the probability of receiving infinitely many units of some good, without differences in the valuation of different infinite payouts, approximates to a bounded utility function, e.g. assigning utility 1 to world-histories with an infinite payout of the good, and 0 to all other world-histories.
A system which selects actions so as to maximize the probability of receiving infinitely many units of some good, without differences in the valuation of different infinite payouts, approximates to a bounded utility function, e.g. assigning utility 1 to world-histories with an infinite payout of the good, and 0 to all other world-histories.