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Asymptotic Equipartition Property

A theorem from information theory that is a simple consequence of the weak law of large numbers. It states that if a set of values X_1, X_2, ..., X_n is drawn independently from a random variable X distributed according to P(x), then the joint probability P(X_1,...,X_n) satisfies

-1/nlog_2P(X_1,X_2,...,X_n)->H(X),

where H(X) is the entropy of the random variable X.

See also

Entropy

This entry contributed by Erik G. Miller

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References

Cover, T. M. and Thomas, J. A. Elements of Information Theory. New York: Wiley, 1991.

Referenced on Wolfram|Alpha

Asymptotic Equipartition Property

Cite this as:

Miller, Erik G. "Asymptotic Equipartition Property." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AsymptoticEquipartitionProperty.html

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