Sup-Sums Principles for F -Divergence and a New Definition for t -Entropy

The article presents new $${\sup }$$ -sums principles for integral F-divergence for arbitrary convex functions F on the whole real axis and arbitrary (not necessarily positive and normalized) measures. Among applications of these results, we work out a new ‘integral’ definition for t-entropy explicitly establishing its relation to Kullback–Leibler divergence.