Title used for the ‘law of large numbers’ in probability theory, proved by Jakob Bernoulli (1654–1705). The theorem provides the best-known link between probability and the frequency of occurrence of events in a sequence of trials. It is thus fundamental to the epistemology of probability. Bernoulli showed that if we have a sequence of n trials, on each of which an outcome has probability p, then the most probable number of times the event occurs is pn (or the nearest integer to this); furthermore for any small number e, the probability that the frequency of occurrence falls within the interval np ± e increases with n, and approaches 1 as n approaches infinity.