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A class of Shannon-Mcmillan theorems for second-order nonhomogeneous Markov information source on generalized random selection systems

Wang Kangkang1,Li Fang2,Meng Yiping3(1.School of Mathematics and Physics,Jiangsu University of Science and Technology,Zhenjiang Jiangsu 212003,China)(2.School of Mathematics and Computer Science,Anhui Normal University,Wuhu Anhui 241000,China)(3.Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China)  
In this paper,a class of generalized Shannon-McMillan theorems for the second-order nonhomogeneous Markov information source on the generalized gambling system are discussed by constructing the consistent distribution and nonnegative supermartingales.As corollaries,some Shannon-Mcmillan theorems for the nonhomogeneous Markov information source,non-momery information source are obtained.
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