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A class of asymptotic equipartition property theorems for arbitrary discrete information source

Wang Kangkang,Xu Weiyan(School of Mathematics and Physics,Jiangsu University of Science and Technology,Zhenjiang Jiangsu 212003,China)  
A class of Shannon-McMillan theorems for the arbitrary information source was studied.The strong limit theorems for relative entropy densities of the sequence of arbitrary random variables were discussed by constructing the compatible distribution,nonnegative superior martingale,and the important inequalities.As corollaries,some asymptotic equipartition property theorems for arbitrary information source,m-order Markov information source,and non-memory information source were obtained.Moreover,some obtained results for the discrete information source were extended.
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