A Closer Look at Talagrand’s Inequality

When presenting Talagrand’s Inequality in Chap. 10, we sacrificed power for simplicity. The original inequality provided by Talagrand is much more general than those we stated, but it is somewhat unwieldy. In this chapter, we will see Talagrand’s original inequality, and we will show how to derive from it the weaker inequalities of Chap. 10. In order to give the reader a better idea of how the full inequality can be used, we will present a few other weakenings that can be derived from it, each one a generalization of those that we already know.