Inequalities and Extremal Problems in Probability and Statistics: Selected Topics

Usually, at the heart of a good limit theorem in probability or statistics is a good inequality - because, in applications, a topological neighbourhood is usually defined by inequalities. This fact needs to be much more widely appreciated. The proposed book aims to promote such appreciation, by presenting various kinds of useful inequalities, applicable in many areas of mathematics, sciences, and engineering. It is oftentimes desirable that the bound provided by the inequality in question be sharp (exact, optimal, best possible) in some sense; in other words, such a bound would present a solution to an extremal problem.