A general result in measure theory that is a particularly useful application when applied to a probability measure. If {A_n} is an infinite sequence of measurable sets, where the sum of the measures ${\displaystyle \sum _{n=1}^{\infty }}\mu (A_n)$ is finite, then the set of points which lie in an infinite number of the sets must have measure zero. If the A_n are events in a probability space, then the probability that infinitely many of the events occur is zero. A related result shows that if the events are independent and the sum of their probabilities is infinite, then the probability that infinitely many of the events occur is one.