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The article presents new    $${\sup }$$  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.

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