We prove the Borel-Cantelli Lemma, which states that if a countable sum of the probabilities of events is finite, then the set of points which belong to infinitely many of these sets is zero. Equivalently, the probability of the limit superior of these sets is zero. This Lemma while elementary to prove is extremely important in the study of random series and stochastic processes.
#mikethemathematician, #mikedabkowski, #profdabkowski
