The structure of the I-measure of a Markov chain

Abstract

The underlying mathematical structure of Shannon's information measures was studied in a paper by R.W. Yeung (1991), and the I-Measure mu *, which is a signed measure defined on a proper sigma -field F, was introduced. The I-Measure is a natural extension of Shannon's information measures and is uniquely defined by them. They also introduced as a consequence the I-Diagram as a geometric tool for visualizing the relationship among the information measures. In general, an I-Diagram for n random variables must be constructed in n-1 dimensions. It is shown that for any finite collection of random variables forming a Markov chain, mu * assumes a very simple structure which can be illustrated by an I-Diagram in two dimensions, and mu * is a nonnegative measure. >