Consider an infinite set E(G) where the elements are interpreted as independent events assigned probabilities under a Gaussian distribution. It can be shown that the probabilities of all events in E(G) will sum to one. Now consider an infinite set E(U) with the same interpretation under a uniform distribution (every event has equal probability). Given an infinite set, this implies that the probability of any randomly chosen event in E(U) is zero. Is it then true that for any continuous uniform probability distribution, the sum of probabilities will be zero?