The Limit Properties of a Class of Averages of Functions of Two Variables of Arbitrary Information Sources

In this paper, the notion of the relative entropy density deviation of arbitray information source, relative to Markov information sources, is introduced, and some limit properties of the averages of the functions of two variables of arbitrary m-valued information source are studied by using this notion. As a corollary of the main result, an extension of Shannon-McMillan Theorem is obtained.