Riesz Representation Theorem

A family of results identifying continuous linear functionals on particular function spaces with concrete representers: on a Hilbert space every continuous linear functional is inner-product with a unique element; for certain continuous function spaces, duals correspond to measures.

A theorem that characterizes continuous linear functionals on certain topological vector spaces by concrete objects: on a Hilbert space H every bounded linear functional is given by the inner product with a unique vector in H, and on C0(X) (continuous functions vanishing at infinity on a locally compact Hausdorff space X) every continuous linear functional is represented as integration against a u