Representation theorem
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In mathematics, representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract or concrete) structure.
In mathematics, representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract or concrete) structure. The Riesz representation theorem states that a Hilbert space, such as the square-integrable function space L 2 (X) on a manifold X, any linear functional F is equal to the inner product with a fixed element a\in H , i.e. F(v) = \langle a,v\rangle for all v\in H . The more general Riesz–Markov–Kakutani representation theorem has several versions, one of them identifying the dual space of C 0 (X) with the set of regular measures on X.
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