Shannon-McMillian-Breiman theorem

Shannon-McMillian-Breiman theorem

[′shan·ən mik′mil·ən ′brī·mən ‚thir·əm]
(mathematics)
Given an ergodic measure preserving transformation T on a probability space and a finite partition ζ of that space the limit as n →∞ of 1/ n times the information function of the common refinement of ζ, T -1ζ, …, T -n + 1ζ converges almost everywhere and in the L1 metric to the entropy of T given ζ.