The Borel–Cantelli lemma

18.06.2020 09:30 - 09:50

Larisa Yaroslavtseva (Universität Ulm)


The Borel–Cantelli lemma is a theorem about the probability that infinitely many of events from a given sequence of events A1, A2, . . . occur. It is an important tool frequently used in connection with questions concerning almost sure convergence. In this lecture we formulate and prove the Borel-Cantelli lemma. We furthermore provide examples to illustrate its application. One of the examples is the infinite monkey theorem, which states that with probability 1 a monkey hitting keys at random on a typewriter for an infinite amount of time will type the complete works of William Shakespeare infinitely often.

Fakultät für Mathematik
Zoom Meeting