The Borel-Cantelli Lemma is a fundamental result in probability theory that helps determine the behavior of sequences of events. It states that if the sum of the probabilities of a sequence of events is finite, then the probability that infinitely many of those events occur is zero. In simpler terms, if you have a series of events that happen less and less frequently, they will almost surely stop happening altogether. Conversely, if the events are independent and the sum of their probabilities diverges (i.e., is infinite), then the probability that infinitely many of those events occur is one. This means that if the events are frequent enough, they will almost surely happen infinitely often. The lemma is named after mathematicians Émile Borel and Georg Cantelli.