Uniform Logical New Proofs for the Daniell–Stone Theorem and the Riesz Representation Theorem

Topological Vector Spaces ◽

I this paper we establish a Riesz representation type theorem which characterizes the dual of the space C rc (X,E)endowed with the countable-ope topologyi the case of E ot ecessarilya locallyconvex TVS.

A generalization of inverse distance weighting and an equivalence relationship to noise-free Gaussian process interpolation via Riesz representation theorem

Linear and Multilinear Algebra ◽

10.1080/03081087.2017.1337057 ◽

2017 ◽

Vol 66 (5) ◽

pp. 1054-1066 ◽

Cited By ~ 2

Author(s):

Wim De Mulder ◽

Geert Molenberghs ◽

Geert Verbeke

Keyword(s):

Gaussian Process ◽

Representation Theorem ◽

Inverse Distance Weighting ◽

Distance Weighting ◽

Riesz Representation ◽

Equivalence Relationship ◽

Inverse Distance

A note on the Riesz representation theorem

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1963-0145334-0 ◽

1963 ◽

Vol 14 (2) ◽

pp. 354-354 ◽

Cited By ~ 9

Author(s):

Don H. Tucker

Keyword(s):

Representation Theorem ◽

The Riesz Representation Theorem and Integral Norms

Journal of the London Mathematical Society ◽

10.1112/jlms/s1-43.1.177 ◽

1968 ◽

Vol s1-43 (1) ◽

pp. 177-182 ◽

Cited By ~ 1

Author(s):

B. L. D. Thorp

Keyword(s):

Representation Theorem ◽

Appendix Measures and the Riesz Representation Theorem

Convex Cones - North-Holland Mathematics Studies ◽

10.1016/s0304-0208(08)71029-6 ◽

1981 ◽

pp. 380-401

Keyword(s):

Representation Theorem ◽

Yet another short proof of the Riesz representation theorem

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100001456 ◽

1989 ◽

Vol 105 (1) ◽

pp. 139-140 ◽

Cited By ~ 1

Author(s):

David Ross

Keyword(s):

Representation Theorem ◽

Short Proof ◽

Riesz Theorem ◽

F. Riesz's ‘Representation Theorem’ has been proved by methods classical [11, 12], category-theoretic [7], and functional-analytic [2, 9]. (Garling's remarkable proofs [5, 6] owe their brevity to the combined strength of these and other methods.) These proofs often reveal a connection between the Riesz theorem and some unexpected area of mathematics.

A nonstandard proof of the Riesz representation theorem for weakly compact operators on C(Ω)

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100001468 ◽

1989 ◽

Vol 105 (1) ◽

pp. 141-145

Author(s):

Yeneng Sun

Keyword(s):

Representation Theorem ◽

Compact Operators ◽

Linear Functionals ◽

Weakly Compact ◽

Vector Measures ◽

Riesz Representation ◽

Weakly Compact Operators ◽

Measure Technique

AbstractAn easy way to construct the representing vector measures of weakly compact operators on C(Ω) is given by using the Loeb measure technique. This construction is not based on the Riesz representation theorem for linear functionals; thus we have a uniform way to treat the scalar and vector cases. Also the star finite representations of regular vector measures follow from the proof.