 Riesz representation theorem

Every bounded linear functional on a Hilbert space is inner product with one unique vector, with equal norms.

The Riesz representation theorem is a fundamental result in functional analysis that characterizes certain types of linear functionals on a space of continuous functions. The most commonly referenced version of the theorem deals with the space of continuous functions on a compact Hausdorff space, often denoted as \( C(X) \), where \( X \) is a compact Hausdorff topological space.