In measure theory, if we have a countably infinite group of sets, then all of them is a measurable set.This means that yes/no questions that depend on countably many coordinates have a probabilistic answer.
In measure theory, if we have a countably infinite collection of measurable sets, then the union and intersection of all of them is a measurable set. For our purposes, this means that yes/no questions that depend on countably many coordinates have a probabilistic answer.