Shannon-McMillian-Breiman theorem

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Shannon-McMillian-Breiman theorem [′shan·ən mik′mil·ən ′brī·mən ‚thir·əm]

(mathematics)

Given an ergodic measure preserving transformationTon a probability space and a finite partition ζ of that space the limit asn→∞ of 1/ntimes the information function of the common refinement of ζ,T^-1ζ, …,T^{-n + 1}ζ converges almost everywhere and in theL₁metric to the entropy ofTgiven ζ.

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