##  [Riesz Representation Theorem](/riesz-representation-theorem) 

  ##  [Riesz Representation Theorem](https://mathlogic.quantumdictionary.io/riesz-representation-theorem-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.

 

 

 

 

 





 

 



 ##  [Riesz Representation Theorem](https://puremath.quantumdictionary.io/riesz-representation-theorem-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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