A note on the Riesz representation theorem

The Riesz representation theorem

A Formal Proof Of The Riesz Representation Theorem

This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation...

The Orthogonal Projection and the Riesz Representation Theorem

In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real ...

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

A Riesz Representation Theorem for Cone-valued Functions

The theory of locally convex cones, as developed in [3], deals with ordered cones that are not necessarily embeddable in vector spaces. A topological structure is introduced using order theoretical concepts. We will review some of the main concepts and globally refer to [3] for details and proofs. An ordered cone is a set endowed with an addition and a scalar multiplication for nonnegative real...