A new outlook on Shannon´s information measures

The author presents a new approach to understanding the underlying mathematical structure of Shannon´s information measures, which provides answers to the following two questions for any finite number of random variables. (1) For any information-theoretic identity, is there a corresponding set-theoretic identity via the formal substitution of symbols? (2) For any set-theoretic identity, is there a corresponding information-theoretic identity and, if so, in what sense? The author establishes the analogy between information theory and set theory. Therefore, each information-theoretic operation can formally be viewed as a set-theoretic operation and vice versa. This point of view, which the author believes is of fundamental importance has apparently been overlooked in the past by information theorists. As a consequence the I-diagram, which is a geometrical representation of the relationship among the information measures, is introduced. The I-diagram is analogous to the Venn diagram in set theory. The use of the I-diagram is discussed.