Bounds of Generalized ‘Useful’ Information Measure With Application of Jensen's Inequality

‘Useful’ information measure is one of the generalizations of Shannon’s entropy when utilities are attached to probabilities. The classical state of Jensen’s inequality comprises many numbers and weights. The inequality can be expressed quite mostly using either the communication of measure theory or chance. In the probabilistic mounting, the inequality can be far general to its overladen power. In this chapter, first, ‘useful’ information measure and Jensen’s inequality along with utility are defined and explained. A convex function is considered, and then lower and upper bounds for Jensen’s inequality along with utility are developed. We also establish bounds on Shannon’s information measure with application of bounds obtained for Jensen’s inequality.