# The Law of the Iterated Logarithm in Probability Theory

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The law of the iterated logarithm is a refinement of the strong law of large numbers, a fundamental result in probability theory. In the particular case of an unlimited sequence of Bernoulli trials with parameter , the strong law asserts that with probability one, the relative frequency of successes converges to *p* as the number of trials grows.

Contributed by: Tomas Garza (December 2007)

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The main reference for this topic is W. Feller, "Unlimited Sequences of Bernoulli Trials: The Law of the Iterated Logarithm," *An Introduction to Probability Theory and Its Applications*, Vol. 1, New York: John Wiley & Sons, Inc., 1970 pp. 204–208.

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