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The article presents new sup-sums principles for integral F-divergence forarbitrary convex function F and arbitrary (not necessarily positive andabsolutely continuous) measures. As applications of these results we derive thecorresponding sup-sums principle for Kullback--Leibler divergence and work outnew `integral' definition for t-entropy explicitly establishing its relation toKullback--Leibler divergence.

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