1. I-Measure

2. Recall Shannon’s Information measures

4. The Chain Rules

5. Markov Chains

7. A Signed measure function and its properties.

8. I-measure and Signed measure

13. The I-measure and Signed measure Hence we can clearly see the one to one correspondence between Shannon’s information measure and set theory in general.

14. Applications of the I- measure

16. Information diagram The one to one relations between Shannon’s information measure and set theory suggest that we should be able to display Shannon’s information measures in an information diagram using Venn diagram. But actually for n random variable we need a n-1 dimension to completely display all of them. On the other hand when the random variable that we are dealing with form a markov Chain, 2 dimensions is enough to

17. Information diagram

18. References Book: Fundamentals of Real Analysis Sterling K, Berberian Book : A first course in Information Theory Raymond W, Yeung. The Chinese University of Hong Kong