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Inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics, ergodic theory, and other scientific fields. We suggest new inequalities of this type, often based on underlying identities. As a consequence, we obtain certain improvements of the well-known Pinsker inequality. Our study depends on two measures of discrimination, called capacitory discrimination and triangular discrimination. The discussion contains references to related research and comparison with other measures of discrimination, e.g., Ali-Silvey-Csiszar (1996, 1966) divergences and, in particular, the Hellinger distance.
Flemming Topsøe (Sat,) studied this question.