Sup-sums principles for F-divergence, Kullback--Leibler divergence, and new definition for t-entropy

The article presents new sup-sums principles for integral F-divergence for arbitrary convex function F and arbitrary (not necessarily positive and absolutely continuous) measures. As applications of these results we derive the corresponding sup-sums principle for Kullback--Leibler divergence and work out new `integral definition for t-entropy explicitly establishing its relation to Kullback--Leibler divergence.