The asymptotic equipartition property for Mth-order nonhomogeneous Markov information sources

In this correspondence, we first establish a limit theorem for averages of the functions of m+1 variables of mth-order nonhomogeneous Markov information sources. As corollaries, we obtain several limit theorems for frequency of occurrence of the states and a limit theorem of the entropy density for these information sources. Finally, we prove the asymptotic equipartition property (AEP) for a class of nonhomogeneous Markov information sources.