# PTAH inequality result

There is an additional classic inequality to be added to the list (A) through (F), namely the maximum-entropy inequality (in logarithmic form)

 $-\sum_{i=1}^{n}p_{i}\log p_{i}\leq\log n.$

Also, inequality (C) should be labeled “the Kullback–Leibler inequality”.

Then, the labeling could be modified: the first time the PTAH inequality appears it could be labeled (P); then the maximum-entropy inequality could be labeled (G), followed by Hölder’s inequality (already labeled (H)); and the statement could be “the inequalities (A) through (G) are equivalent, each is a special case of (H), and (H) is a special case of (P). However, it appears that none of the reverse implications hold.”

Title PTAH inequality result PTAHInequalityResult 2013-03-22 18:08:33 2013-03-22 18:08:33 cappymate (20671) cappymate (20671) 4 cappymate (20671) Result msc 26D15