Non-Shannon-type Inequalities
Other, less trivial inequalities have been discovered among the entropies and joint entropies of four or more random variables, which cannot be derived from Shannon's basic inequalities. These are known as non-Shannon-type inequalities.
It was shown that
where the inclusions are proper for The last two sets are, in fact, convex cones.
Read more about this topic: Inequalities In Information Theory
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“The only inequalities that matter begin in the mind. It is not income levels but differences in mental equipment that keep people apart, breed feelings of inferiority.”
—Jacquetta Hawkes (b. 1910)