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As a consequence, we obtain lower bounds in terms of $V$ for many well known distance and divergence measures. For instance, let $D_{(\\alpha)} (P,Q) = [\\alpha (\\alpha-1)]^{-1} [\\int q^{\\alpha} p^{1-\\alpha} d \\mu -1]$ and ${\\cal I}_\\alpha (P,Q) = (\\alpha -1)^{-1} \\log [\\int p^\\alpha q^{1-\\alpha} d \\mu]$ be respectively the {\\em relative informatio","authors_text":"Gustavo L. Gilardoni","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2006-03-24T11:47:59Z","title":"On Pinsker's Type Inequalities and Csiszar's f-divergences. 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