Riesz representation theorems belong to the family of results on duality in Banach space theory. Given a Banach space, the identification of its dual space is useful in various situations. It turns out that several concepts already introduced in this book can be seen as duality results in functional analysis. For example Hölder’s inequality is an inequality that describes the duality between Lp spaces. Moreover, the extension theorem for measures can be interpreted as the description of the dual space of the space of continuous functions on a compact set.